Wenger looks set to stay at Arsenal after reportedly agreeing to sign a new two-year deal with the club.
Gunners fans look to be split on the decision, with many supporters protesting against him throughout the course of the campaign.
Arsenal ended a difficult season on a high at the weekend, beating Chelsea 2-1 at Wembley to win the FA Cup.
However, they missed out on a place in the Champions League for the first time in 21 years – finishing just behind fourth-placed Liverpool.
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Arsene Wenger looks set to stay on as Arsenal manager
Arsenal have got a long way to go at the moment, they're further behind than Arsene Wenger thinks
And they also finished behind fierce rivals Tottenham – something that last happened back in 1995.
Despite their troubles, and the fact Borussia Dortmund parted company with Thomas Tuchel, Wenger looks likely to extend his Emirates stay.
But Lineker has questioned that decision, saying Arsenal are a lot further behind their Premier League rivals than people think.
"Arsenal have got a long way to go at the moment, they're further behind than Arsene Wenger thinks," Lineker told BBC Radio 5 live.
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Arsene Wenger steered Arsenal to FA Cup glory on Saturday
"If you ask me now whether Arsenal are going to be in the top four next season, I would say most probably not.
"Wenger was still winning FA Cups and until this season he had always got in the top four, but now that's changed.
"I just hope if and when he decides to go he kind of does himself because I don't want people to feel badly about him and I hope he doesn't spoil that.
"But I sense he's going to stay anyway, so let's see what happens."