Manchester City boss Roberto Mancini is confident the £25million summer signing has learnt the lessons of past mistakes and will keep the focus purely on the football against his old club.
Adebayor was handed a three-match ban for raking his studs down the face of Arsenal forward Robin van Persie which followed an ill-advised goal celebration - an action which resulted in a suspended two-game sanction and a £25,000 fine from the Football Association.
The former Togo international raced the full length of the field to slide right in front of the Gunners' supporters during the clash at Eastlands back in September.
Wenger, who plucked Adebayor from relative obscurity at Monaco in January 2006 and helped turn him into one of the hottest properties in Europe, believes all that should be left in the past.
The Arsenal boss said: "I am stubborn, but not stupid - sometimes in the heat of the moment you can do things that are not right.
"It is not only Adebayor, but also Patrick Vieira and Kolo Toure - we will welcome them all back.
"We have always had the same line of conduct - to respect what they have done for us and we want our fans to respect that as well and encourage our team.
"No matter what happened in the first game, it is important that we have a positive attitude and encourage our players.
"I believe more than ever we will need the crowd to be behind us. I expect everybody to behave well."
Arsenal's hopes of staying in the Premier League title race were thrown away during a ridiculous final 10 minutes at Wigan on Sunday, when they allowed a 2-0 lead to slip as the home side fought back to win.
"Our pride is to fight until the end and this season we have shown a lot of fighting spirit, even if we had two disappointing results," said Wenger.
"It is important that we keep fighting, because you never know - and also we are as well under threat from the people chasing from behind. Nothing is secure."
With first-choice goalkeeper Manuel Almunia again out with a wrist injury, Wenger looks set to give Lukasz Fabianski a chance to redeem himself after a glaring error gifted Wigan an equaliser.
Despite a series of high-profile blunders this season - including away to Porto in the Champions League and in the FA Cup defeat at Stoke - the young Pole continues to have complete confidence of his manager.
"I think he will be a great keeper," Wenger maintained. "If you ask how many mistakes you can afford, I would say zero, but also it is part of the game.
"I believe Fabianski has great quality and spirit. He has a good opportunity to show how good he is.
"Of course, he was disappointed on Sunday, but I believe he was not the only one involved in our defeat."
It has been suggested Arsenal will look to bring in a new goalkeeper during the summer and have been linked with England youngster Joe Hart, currently on loan from City at Birmingham.
Wojciech Szczesny, who has just turned 20, believes he can return from a loan spell at Brentford ready to challenge for a place in the Arsenal first team.
Wenger said: "It is reasonable to have the ambition to be number one here next season and he is doing extremely well.
"I believe one day he will be the number one at Arsenal certainly, but we will see next season.
"It is down to his performances - but you also want some experience at our level. You cannot only go with young goalkeepers."
Wenger has long championed the promise of youth, but is a policy which has failed to deliver a trophy since the 2005 FA Cup.
The Arsenal manager is likely to strengthen the squad in the summer, with Morocco striker Marouane Chamakh expected to arrive on a free transfer from Bordeaux.
However, Wenger maintains this campaign, which has been blighted by injury to key men, can be seen as progress.
He said: "We have moved forwards, and with the age of the team, there is still some room for improvement."