But the new manager Bruce Rioch, who would not confirm Jensen has been offered a better deal, is expecting him to sign when he returns to Highbury on Friday.
Jensen, signed in the summer of 1992 after scoring one of Denmark's goals in their European championship final victory over Germany, has become best known as the player whose transfer caused the downfall of George Graham, the former Arsenal manager, in the infamous "bungs" affair.
He seemed to have no further part to play for Arsenal at the end of his contract last season, having been left out of the side which lost to Real Zaragoza in the European Cup Winners' Cup final. His situation had been closely monitored by his former club, Brondby, but he has surprised many by appearing in all Arsenal's pre-season games since Rioch took charge in June.
Meanwhile, David Platt, Arsenal's pounds 4.75m capture from Sampdoria, has pledged to cut down on his large schedule of personal engagements once the season begins.
Platt, who yesterday helped launch a new Premier League sponsorship tie- up with McDonalds, the fast food giant, said: "I feel it was important to be involved in this one as it is for the general good of football. It is an idea to boost the attendances of younger people at matches and most of the money from the deal is being steered towards facilities for families at stadiums.
"But I don't want to become over-involved in too many projects. It is a case of choosing the right ones to go for."
He is putting 100 per cent into being fit for the start of the season against Middlesbrough at Highbury on Sunday, and is shrugging off suggestions that a knee injury he aggravated in last Thursday's goalless draw against Internazionale is threatening his place in the side.
"I came off in that match purely because it did not make sense to continue when I felt a little bit of discomfort," he said.
The deal with McDonalds is worth pounds 7m over the next four years to Premier League clubs, provided a two-year option is taken up after the first two years of the deal.
Nearly pounds 1m of the pounds 1.75m on the table for each season will go towards improving family enclosure facilities at the Premier League clubs.
But Rick Parry, the Premier League chief executive, could not guarantee that it would lead to cheaper admission for youngsters.Reuse content