Wenger's future – not for the first time – has been shrouded in uncertainty with the Frenchman yet to say whether he will still be in charge next term.
Juventus boss Max Allegri and Thomas Tuchel of Borussia Dortmund have both been touted as possible successors.
Arsenal face Hull tomorrow (12.30pm) and a defeat could see them fall out of the top four by the end of the afternoon.
Who could succeed Arsene Wenger at Arsenal?
Wed, February 8, 2017
Express Sport takes a look at top candidates who could replace Arsene Wenger at Arsenal
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Who are the favourites to replace Arsene Wenger at Arsenal?
Arsene Wenger's future at Arsenal is uncertain
Arsenal slumped to a 3-1 defeat to Chelsea last weekend
And Graham believes Wenger will assess his future if Arsenal fail to challenge for trophies this season.
"It could be the end," Graham told talkSPORT.
"The decision will be Arsene's. The club won't make a decision like that.
George Graham managed Arsenal for nine years
"They'll get together and work it out. He will leave the way he should leave.
"They've won a few FA Cups that Tottenham would be delighted with but they've set the bar high and I think the league and the European Cup are the ones they want to win.
"Arsenal are a big club in world football and should be going for the big trophies, including the European Cup."