Tosic has spent time out on-loan at Bundesliga outfit Cologne since January but is set for a return to his parent club after the deal expired.
The German side said they were keen on keeping hold of the Serbian for the new campaign but could see their attempts scuppered as it emerged United were looking to off-load the 23-year-old.
The Red Devils are said to be eyeing up a £4million deal should they choose to sell the winger and are reportedly not interesting in arranging a new loan agreement for his services.
Tosic's loan spell had no option to buy the player upon its expiry, meaning the former Serbian under-21 international could move elsewhere.
The United star netted five times in 14 appearances at the RheinEnergie Stadion outfit and chairman Wolfgang Overath says he is doing his upmost to keep hold of the player ahead of the new campaign.
He told German newspaper Express: "We are fighting to keep the player.
"I think we are the first club in any line, should it be up to Zoran (Tosic). That was what he has told us in person.
"We are definitely trying our very best to get him going on at our club."