The Portuguese winger was considering his future earlier this month and The Sun claims that his poor performances towards the end of last season could force him out of the club.
A Red Devils source told the newspaper: "The club did not think his form at the end of last season put him in a very strong bargaining position over a new deal.
"Right now United are happy to leave it until next summer unless his demands are dramatically dropped. But they won't sell unless silly money comes in."
Nani's contract expires in 2014 and United will reportedly only accept a bid that matches their valuation for the 25-year-old.