The Republic of Ireland international announced on Thursday that he felt this would be the last season of his 12-year career at United and that he would leave the Premiership next summer.
Keane, who signed from Nottingham Forest in the summer of 1993 for a then British record fee of £3.75m, is in the final year of his current deal and believes it will not be renewed.
However, the Arsenal manager Wenger feels the 34-year-old, who has inspired his club to seven Premier League titles and four FA Cups, could be trying to entice one last contract out of the United board.
Wenger said: "We will not bid for him in January. He has played his whole career [sic] at United and I am not convinced yet that he will leave. Of course, he could be saying to them, 'Come on Manchester United, if you want to keep me one more year it's time to wake up because I have some other offers on the table'. So he could still finish up staying."
But Wenger did agree that even though Keane's powers are on the wane, it would be as big a blow to United to lose him as it has been for the Gunners to lose Patrick Vieira, whom they sold to Juventus in the summer for £13.5m. The Frenchman said: "It is significant for Manchester United that he has said he will leave. He was a big player for them and he is coming to the end of his career. But you know at the start he will not last for ever.
"Of course it will be as hard for them to replace him as it is for us to replace Vieira. It will be hard. The difficulty for Manchester United is that Roy Keane is not the player he was but he is still a good player.
"What is difficult for United is to evaluate how long he can keep going on. In the big games he always plays because he is still a very good player, even if he is not the player he was when he was 28 or 29. But he is still a very useful player at United so it will be a loss."
Arsenal will give fitness tests to Gilberto and Dennis Bergkamp ahead of their game against Birmingham at Highbury tomorrow.
Bergkamp is rated at "80-20" to recover from back and groin injuries but should still only make the substitutes' bench. Gilberto has little chance of recovering, according to Wenger, while Philippe Senderos and Thierry Henry are still out.
The Blues are also injury-ravaged, with only 13 senior players fit to make the trip. But the manager Steve Bruce still has enough scope in his squad to replace £3m summer capture Mikael Forssell with Walter Pandiani, who will partner Emile Heskey in attack.Reuse content