Rooney, who scored in England's 2-2 draw with Brazil, handed in a second transfer request in three seasons, former United manager Sir Alex Ferguson confirmed last month.
The 27-year-old was left out of United's squads for the final two matches of an underwhelming campaign, with Rooney's role in the team a priority for new manager David Moyes to address.
Since he was omitted from the starting XI for United's Champions League round-of-16 tie at home to Real Madrid in March Rooney has been linked with a move away from Old Trafford, with Paris St. Germain confirmed admirers.
Arsenal are a more intriguing name bracketed with the England international, who has scored 12 times against the Gunners in his career for Everton and United, and Wenger admitted Rooney would be an "interesting" signing.
"Rooney could be an interesting player for everybody in the world, who would turn him down?" the Frenchman told Al Jazeera.
"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."
Wenger is believed to be armed with a £70 million budget to end Arsenal's trophy drought, which is nearing a decade, and a consistent goalscorer is a priority for the Gunners.
Despite respectable campaigns, neither Lukas Podolski or Olivier Giroud appear capable of shouldering the burden as the team's main striker, which has seen Real Madrid's Gonzalo Higuaín also emerge as a possible target.
Rooney's finest seasons in a United shirt have come as a lone striker, when he scored 34 goals in both the 2009-10 and 2011-12 campaigns.