The financially well-off club have £200 million to spend, according to the Daily Mail, and are keen to bring in Nasri as an eventual replacement for compatriot Franck Ribery, who is nearing the end of his current contract.
This will make Arsenal manager Arsene Wenger's task of keeping the 23-year-old even tougher, given that Bayern, the fourth richest club in the world, can afford to give Nasri a pay-check he cannot refuse.
However, United will certainly not give up in their pursuit for the player, as their other targer, Inter Milan's Wesley Sneijder, has asked for £250,000-a-week in order to join the Red Devils.
United are also losing interest in Everton midfielder Jack Rodwell, who is now a target for Tottenham Hotspur instead.
According to reports from the Independent, the current Barclays Premier League champions will try to snap up the Frenchman at a bargain £8 million, as Nasri has only one year left on his current deal with the Gunners.
Both United and Nasri's representatives met up in Manchester on Thursday, and this latest development will not be good news for Gunner manager Arsene Wenger, who will now have to decide if he should keep the player on his contract based on principle, or sell him to ensure that the London side does not miss out on a valuable transfer fee.
Is Samir Nasri on his way out from the Emirates?