Wenger's men led 2-0 with ten minutes remaining before Roberto Martinez’s side scored three late goals to end their title hopes.
"Arsene's current contract ends at the end of next season and when Arsene says he has yet to decide whether to stay, I do actually believe him," Wright wrote in his column for The Sun.
"I think he is still mulling over whether he wants an extra couple of years at the club."
Arsenal have not won a trophy since beating Manchester United in the 2005 FA Cup final and Wright believes supporters may want a change of manager following their lack of silverware in recent years.
"After yet another season without a trophy - it's five years now - there is a split between the supporters who wants him to remain and those who want a change," he added.
"I reckon it's now about 50-50."
While Wright admits the defeat to rivals Tottenham and the Champions League exit at the hands of Barcelona were disappointing, he believes Wenger will have to invest in the summer if they are to progress, asuming the Frenchman stays.
"While the defeats to Barcelona and Spurs were disappointing, the capitulation in the final 10 minutes at Wigan proved Arsene Wenger's side needs some major surgery," he said.
"And now it's time for Arsene to be honest with the fans.
"All my Arsenal mates keep asking me what's going on - and all Arsenal fans deserve to hear the truth.
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