Nicholas, who played for both clubs in his playing career, thinks the former Liverpool boss has boosted his reputation since taking the Celtic job ahead of the 2016-17 season.
Wenger is facing an uncertain future at Emirates Stadium, with his contract due to expire at the end of the campaign. The Frenchman says he has made his decision on his future, but is yet to announce it publicly.
Whether or not Wenger ultimately goes this season or in the future, Nicholas thinks Rodgers should be in the conversation to replace him when the time comes.
"I apologise now to Celtic fans because they will be on my case, but of course he would [be a contender]," Nicholas said to Sky Sports.
"He has been different class. He is on a decent salary and he has deserved it and merited it. But absolutely, if Arsenal are looking at a list of names to replace Arsene, Rodgers would be on it.
"He plays the Arsenal way. He played the same style at Liverpool and he probably should have won the league. Everything is there for me to say 'absolutely'."
Celtic are unbeaten in all 29 of their Scottish Premiership matches this season and still in with a chance of winning the treble for the first time since 2001.
"He is building his stock back up," Nicholas said of Rodgers.
"It has been interesting because Celtic have won the title without really working hard for it. He has impressed. He has got good energy.
"He went to win things at Celtic and he has got two trophies in the cabinet already, potentially a third is staring him in the face with the Old Firm derby [in the Scottish Cup semi-final] coming up."
Nicholas thinks Rodgers deserves credit for his work in the transfer market and his development of the players who were already at Celtic before his arrival.
He continued: "Scott Sinclair was struggling in England and he has made him grow again and Moussa Dembele for £500,000 was good value for money.
"But it is the progress of young talent, players like Stuart Armstrong, who for me is the player of the year in Scotland this season.
"He is the most improved player I have seen and it has been such a quick turnaround under Rodgers. Compliments to the players but Brendan has been absolutely fabulous."