The 27-year-old - who said he was "mentally tired" of London life - has claimed "serious negotiations" were already under way with the Spanish club, and a £13million switch close to completion.
Wenger has been keen to keep all of his squad together - including last season's top scorer Emmanuel Adebayor, who remains a target for both Barcelona and AC Milan.
However, the Arsenal manager always has a back-up plan, having already brought in promising Wales teenager Aaron Ramsey to someway offset the departure of midfielder Mathieu Flamini
Nasri revealed he was ready to repay the faith of the renowned French coach.
"Arsene has a great reputation and has proved that he puts a lot of confidence in the young players and he gives them a chance," said the 21-year-old France international.
"It was very important for me to have such a great manager to work with."
Nasri - who has joined the Gunners on what is described as a 'long-term contract' for an undisclosed fee, understood to be around £12million, from Marseille - feels he has all the qualities to fit right in with the culture of "amazing football" at Emirates Stadium.
"I like offensive, technical and quick football - exactly in the style of Arsenal," he declared.
"I hope I will integrate myself quickly in this team and bring everything I can to Arsenal and the fans."