The Tottenham boss, who was cleared yesterday of tax evasion charges, is the firm favourite to replace Fabio Capello, who resigned last night after talks with Football Association chairman David Bernstein.
Redknapp spoke as he left his home near Poole today, and played down talk of him stepping in to guide the team at Euro 2012.
He said on Sky News: "I've not even thought about it. I've got a job to do.
"I've got a big game on Saturday for Tottenham. Tottenham is my focus."
Tottenham face Newcastle at the weekend, and Redknapp insists all his attention is on that fixture.
Asked whether he could help out England this summer, Redknapp said: "I've never thought about it.
"They (the Football Association) will make whatever decision they want to make.
"Hopefully it'll be the right decision for the country but my focus is all on Tottenham."
Capello dramatically resigned over the FA's decision to go over his head and strip John Terry of the England captaincy.
The FA took that action after Terry's trial for allegedly racially abusing Anton Ferdinand was scheduled for July, after the Euro 2012 finals. Terry denies the offence.
Although Capello was known to be frustrated by the FA's move, the Italian's decision to walk away caught many, including Redknapp, by surprise.
Redknapp said: "I was shocked. I was surprised. I didn't expect that to happen.
"We knew he was going to leave in the summer. I didn't expect it to happen now."
Redknapp has been in charge at Tottenham since October 2008, when he took over a team sitting bottom of the Premier League.
He soon lifted the team clear of danger and has since led them to a Champions League quarter-final, while they are involved in the Premier League title battle this season.
"Tottenham have been fantastic to me," Redknapp said from his car today, as he stopped for waiting reporters.
"The fans last week at the Wigan game ... it was incredible the reception they gave me.
"It wouldn't be right for them, (for me) to focus on anything else but Tottenham.
"That's my only interest, is Tottenham Hotspur."
Rio Ferdinand took a farewell swipe at Capello today as he joined Wayne Rooney in endorsing Redknapp to become England's new manager.
The Manchester United and England defender said the national team "don't need anything else lost in translation", an apparent dig at Capello, whose poor command of the English language saw him face criticism during his four years in charge.
Former England captain Ferdinand, who has turned down the chance to take over from Terry as national team skipper, believes Redknapp, his former West Ham boss, is the man best suited to succeed Capello.
He wrote on Twitter: "I think we need an English manager now, we don't need anything else lost in translation....Harry Redknapp would be my choice by a distance."
Striker Rooney wrote on Twitter last night: "Gutted capello has quit. Good guy and top coach. Got to be english to replace him. Harry redknapp for me."
Some will miss Capello, with defender Glen Johnson writing on Twitter this morning: "Sad news to see Capello step down. Good man and a Good manager. £ThanksForEverything."
The FA will hold a press conference at 12pm today at which they are expected to provide more information on Capello's departure.
Sir Keith Mills, a non-executive director at Tottenham, says the club will wait to see what develops regarding Redknapp and the England job.
"I think we're jumping the gun a little bit here," Mills told BBC Radio Five Live.
"Whether Harry will be approached is not a foregone conclusion.
"If he is, then Harry has got a big decision to make."
Former England manager Graham Taylor believes Redknapp is "made for the job" of leading the national team.
Taylor, who succeeded Bobby Robson as England manager after the 1990 World Cup but failed to steer the team to a place in the 1994 tournament, claims 64-year-old Redknapp has the ideal qualities for the position, and is at the right stage in his career.
Taylor told BBC Radio Five Live: "I just think that taking the England job is far better when you're coming towards the end of your career than when you're a young man. I think Harry is in many respects made for the job.
"The public want him, the players want him, sections of the media want him, so that's how it looks at the moment."
Wigan manager Roberto Martinez feels England have lost a good manager whose brilliance will become apparent in time, saying: "I am sure Fabio Capello is going to get the credit he deserves once he is not in the job any longer."
Martinez believes Redknapp has the right qualities to succeed Capello.
He said: "He gets the best out of everyone and that is a great quality to have for a national team coach."
Bolton manager Owen Coyle said: "In my opinion, what England need is somebody to go in and get that spirit together, that camaraderie and to be a motivator.
"Harry Redknapp ticks every box, and he also has fantastic football knowledge. When you put that all together, there is no doubt he is a complete package.
"The difficulty with that is that he has done such a fantastic job with Tottenham Hotspur. I have no doubt - for me, he would be the perfect choice, but I think Tottenham might have something to say about that."
Tottenham's players started their usual training session at 11am at their base in Chigwell without their manager.
A host of photographers and camera crews had assembled outside the Essex training ground but Redknapp was absent, and there was also no sign of his assistant Kevin Bond or Tottenham first-team coach Joe Jordan.
Redknapp told the club yesterday that he would probably not be taking training today as he wanted to rest after his draining 13-day trial.
Stoke chairman and FA Council member Peter Coates wants a home-grown England manager and has joined the long list of people championing the claims of Redknapp.
"Personally I would like the next manager to be English, or at least British," Coates told the Stoke Sentinel.
"I felt Fabio Capello's lack of experience of English football was one of his downfalls.
"His record as a club manager was very impressive but it didn't help that he hadn't got experience here, and he also struggled with the language.
"I wouldn't be in favour of a foreign manager unless, like Arsene Wenger, they had good experience of working in England."
Coates, who tried to take Redknapp to Stoke more than 20 years ago when he was still in charge at Bournemouth, believes the Tottenham boss is probably the ideal candidate to replace Capello.
"I would be very happy with Harry Redknapp if he took the England job," he added.
"He has earned it over a long period of time and produced a lot of good teams.
"But this is all premature at the moment because we don't know if he would take the job now, or whether Spurs would accept losing him."
More on England...
From dentist's chairs to fake sheikhs: England's pre-tournament crises
Fabio Capello: The highs and lows in charge of England
Who's next? The contenders to replace Fabio Capello
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