Evra and United are celebrating after winning the Premier League title this season, and could yet add to that success in the Champions League final against Barcelona on Saturday.
Arsenal, in contrast, are mourning a sixth season without collecting a trophy - with Arsene Wenger promising major changes will be made this summer.
United have reportedly registered an interest in Nasri, whose contract runs out at the end of next season, and Evra believes it would be the right move for his fellow Frenchman to head to Old Trafford.
"Really? I didn't know that," Evra told L'Equipe, when asked about United's interest in Nasri. "Anyway, if he comes, he has to know there is no room for mistakes. Each year you are playing to win. That is Manchester's culture.
"Each year it is a guarantee of a title. I have been at Manchester for five years now and I can't remember how many trophies I have won. 13? 15?
"So, 'Petit Prince', if you want to become King you know where you have to go."