Rooney asked to leave United at the end of last season, and Goal understands he is desperate to leave Old Trafford this summer.
The Gunners have been monitoring the situation regarding the England man, with Chelsea and Paris Saint-Germain also interested, and Wenger has talked up the possibility of a move.
|8/1||Arsenal are 8/1 with Coral to sign Wayne Rooney
"David Moyes' first challenge is to go in to Manchester and bridge the gap between him and Rooney. If that is feasible or not depends on his personality and if Rooney bears a grudge or not, we will see.
"It will be interesting to see how that will be handled."
Arsenal are expected to have around £70 million to spend on transfers this summer, with the club set to agree a new kit deal with Puma.
According to reports on Sunday, however, PSG are willing to offer Rooney £300,000 per week after tax in order to lure him to Parc des Prince.
Wenger also discussed former charge Cesc Fabregas, who has been linked with a move to the Red Devils following a campaign in which he has struggled to nail down a place in the Barcelona first team.
"I think at the moment he's lacking the confidence of being a regular player," he added. "Recently he has not been that.
"Cesc is such a passionate player, a player of such quality, that it must hurt him not to play in every single game. That's what he misses. When you come in and out you never play with full confidence."