The Arsenal captain has rejected a new contract and, although his team want to keep hold of him, the Red Devils boss says that he is one of several managers keen on the striker
The Gunners captain has already pulled out of his club's pre-season tour of Asia in the hopes of forcing a move away as the battle over his future continues.
Premier League champions Manchester City are believed to be closest to the Dutchman's signature, but Sir Alex has revealed that the Red Devils are one of several sides to have their eye on the forward, who has less than 12 months to run on his contract at the Emirates Stadium.
"Obviously Arsenal have given out the fact that we've made a bid for him," he told MUTV.
"We try to keep business as close as possible to us until the moment we conclude a deal. There's no point talking about something that might not happen.
"There are other clubs interested in the player. We've shown an interest and that's where we're at at the moment."
Van Persie scored 36 goals in all competitions for Arsenal in 2011-12, playing a big part in dragging an underperforming side to third place in the Premier League.