The Italian led the West London side to an emphatic Premier League triumph this term following the Blues' poor campaign last season finishing 10th in the top-flight.
Bundesliga giants Bayern Munich and Serie A champions Juventus have also been suggested as potential destinations.
The Arsenal board will meet on Tuesday, before taking their decision to Wenger.
And the Frenchman believes the victory over Antonio Conte's Chelsea is proof enough that he is the right man to continue as Arsenal boss.
"I thought I was playing very, very well in the last few months", he said.
He added: "Look, this season, I think usually we have no sagas". "So that means it's a special night for me".
The goalkeeper, however, tried to adopt a positive approach and said the Chelsea players will try harder to win the FA Cup next year.
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He overtook George Ramsay, who won six FA Cups with Aston Villa between 1887 and 1920, as he secured his seventh success.
"I don't change my commitment", Wenger insisted.
Manager Arsene Wenger has been heavily scrutinised throughout the year but is adamant that Sanchez will remain at the club. "I have nothing against Antonio, he has done a fantastic job". "We go home with a bad taste because of what has happened but for sure we would rather win the Premier League than the FA Cup", said Fabregas. Hopefully one day I'll be back here as a manager, that's kind of the ambition.
The Gunners went into the final with 3 senior defenders out of the clash, leaving just Per Mertesacker as the only senior centre back who hasn't played 90 minutes all season and promising defender Rob Holding who were both exceptional in this match.
"I am a forgiving man", he said.
The fan base certainly seems more divided, with Wenger bemoaning the "very hostile environment" created by some fans demanding his removal.
They either start bright and then fade alarmingly, only to make a late run or they start slowly, then begin to find some form, before extinguishing quicker than a candle in a gale-force wind the moment "pressure" comes on.
"That's why I said it's not about popularity, it's about effect. But I repeat Moses is an honest player and if there was this situation he was exhausted and he didn't want to cheat the referee".