Walcott was a little unsure on the protocol to answering such a question but decided honesty was the best policy. "Yes," he said. "Go on holiday," said Wenger.
If the manager's instruction to his new player was somewhat unusual, it was only in keeping with Walcott's extraordinary rise from primary school to Premiership in six years.
He is, according to some of the game's most experienced managers, unbelievably versatile, has all the ingredients to be a superstar and is a wonderful young man to be around. Oh, and he can walk on water.
Hyperbole, yes. But Wenger and three men who worked with Walcott at Southampton - George Burley, Dave Bassett and Harry Redknapp - are among those queuing up to sing his praises.
"I like the timing of his runs, his determined attitude, the fact that he can play in different positions," said Wenger. "He has all the attributes he will need to go to the very top," said Burley. "He really brightened the landscape," said Bassett. Redknapp came over all lyrical to suggest: "The kid can run through puddles and not make a splash - he drifts over the ground."
Incredibly, Walcott never had any interest in football until he was 10. That was in 1999, when he started to play for Compton Primary School in Berkshire.
"My mate invited me to play because they were short of players and I scored a hat-trick," he said. "I was coming up to 11, I didn't really have a clue how to play, I suppose it just came naturally. I was quite a fast runner and they would put it over the top and I'd run on to it."
He has a knack for understatements. "Quite a fast runner" is a case in point. In 2004, he clocked 11.52sec in a 100 metres race. "It just came naturally," is another. He scored 100 goals in a season for his first junior team, AFC Newbury.
His power, even as a beginner, was also startling. In one warm-up he struck the ball so hard that he broke a goalkeeper's finger.
Football is not the only area where he has shown talent. He plays golf and basketball well, and is also an accomplished painter, although turf, not canvas, will be his medium of expression from now on.
There is some sporting pedigree in his blood. His family tree includes Sir Clyde Walcott, the West Indies cricketing legend whose career highlights included scoring five centuries in three Tests against Australia in 1955.
But neither of Theo's parents, Don or Lynn, were especially sporty. Don is a former British Gas employee and is now an RAF civilian administrator.
He is a Liverpool fan, as is Theo. Lynn is a midwife, and Southampton fan. Theo's sister, Hollie, is a former county netball player, and they also have a brother, Ashley.
Theo's meteoric rise began with a successful trial, while at Compton, for Newbury Schools. He then joined AFC Newbury. His 100-goal season, in 35 games, arrived before he reached his teens.
Swindon snapped him up, and then, rapidly, Southampton came in. Chelsea had also made an offer but the Walcott family preferred the atmosphere at The Dell. He moved there from Swindon, and has lived in digs around the corner from the now-demolished stadium since.
Though he had caused a buzz in coaching circles, he only came to wider prominence last season, and even then, only really among Southampton fans and those who followed the England Under-17 team.
In September 2004, aged 15 years and 175 days, he became the youngest player ever to appear in a senior Saints reserves match, against Watford. He also broke into the England Under-17 side, scoring five times in 11 appearances. After he helped England to beat France 3-1 in a tournament in Portugal in January last year - providing two assists and the third goal - the Under-17 coach John Peacock described him as "superb" and his volleyed strike as "excellent".
Tord Grip, Sven Goran Eriksson's No 2 with England, praised his as "technically very good, and extremely fast as well. He has the ability to beat defenders with his skill, pace and balance".
Walcott also starred as Southampton's promising junior side reached the final of the FA Youth Cup last year, when they lost 3-2 to Ipswich in the two-leg final.
Walcott's senior debut finally arrived, aged 16 years and 143 days, as a 73rd-minute substitute in the Championship match against Wolves on 6 August this season.
He scored his first senior goal - one of four to date - in the 2-1 defeat to Leeds on 18 October. Another of his senior strikes was an audacious lob from wide on the left wing that gave Southampton a 1-0 victory over Luton in December.
Yet it is worth remembering that his entire tally of starts in professional football is still only 13, all in the Championship. He has appeared as a substitute in eight other League games, one League Cup match and the recent FA Cup win over MK Dons.
In December he was on a shortlist of three for the BBC's Young Sports Personality of the Year. In March, he will legally be allowed to drive a car.
What they say about Walcott ...
* ARSENE WENGER, Arsenal manager
Wayne Rooney has achieved a lot and I want to be cautious with comparisons. But he [Walcott] has the same ingredients at the same age to be a big prospect for England. I also like the fact that he is a versatile player who is incredibly dedicated, shows determination and is blessed with electric pace.
* HARRY REDKNAPP, Former manager at Southampton
The kid can run through puddles and not make a splash. He's lightning, he drifts over the ground and he's a fantastic talent. Wherever he goes I'm sure he's got a great future.
* DAVE BASSETT, Former coach at Southampton
A really nice kid. He is very level-headed. He has a nice smile and is obviously doing very well at his football. As for his game, he is a very quick, lively player who has come on the scene and really brightened the landscape.
* SIMON CLIFFORD, Former coach at Southampton
What struck me immediately was just how hard he could strike a football. I've never seen a player hit a ball like Theo - so much power, so much accuracy, with the minimum of back-lift.
* THIERRY HENRY, Arsenal captain
People are saying there are similarities and it's good to hear what he said about me. I've also seen him play this year. I can't even remember what I was like as a player when I was that age so it's difficult to say. But he's a young player with a lot of desire and skills who obviously loves to play football.
* RUPERT LOWE, Southampton chairman
A very gifted young man and I hope he fulfils his potential in the game. He has been a credit to our academy and senior side and goes with our warmest good wishes for his future.
* ANDY COLLING, Walcott's school PE teacher
I've never seen a boy as naturally talented in 19 years of teaching PE. He comes across as self-confident but in no way arrogant. He shied away from attention when he was playing for England Under-17s and we wanted to mention him in assembly. I could see him getting embarrassed.
Falling short: Wenger will be hoping his new arrival will prove better value for money than his other English signings
Arsène Wenger has signed only five English players from other clubs since taking over at Highbury in September 1996, and one of those was Sol Campbell, on a free transfer from Tottenham Hotspur in July 2001. Here is what happened to the four players he paid money for:
* MATTHEW UPSON
Signed as a 17-year-old for £2m from Luton Town in May 1997.
Made 20 League starts in five and a half years - a period when he was loaned out to Nottingham Forest, Crystal Palace and Reading - before being sold at a loss of £1m to Birmingham City in 2003.
* JERMAINE PENNANT
Signed from Notts County for £2m as a 16-year-old in 1999.
Made only two League starts in six and a half years, during which time he was loaned to Watford, Leeds and Birmingham, who supported him after a prison sentence and signed him permanently.
* FRANCIS JEFFERS
Wenger paid Everton £8m in 2001 for the 20-year-old.
Made four League starts in three years. Sold to Charlton at a £5.4m loss in August 2004. Has since made 13 League starts, nine for Charlton and four during an unimpressive loan at Rangers.
* RICHARD WRIGHT
Wenger paid £6m to Ipswich Town for the great hope of English goalkeeping, then 23, in 2001.
Wright made 12 League starts in his one season at Highbury before being sold at a loss of £2.5m to Everton in the summer of 2002.
Total cost to buy: £18m.
Total League starts combined: 38 (£473,684 per League start).
Number of English quartet still at club: 0.
Loss on transfer dealings on four players paid for: £8.9m.Reuse content