Hull City and Celtic are reportedly keen on the striker, with the former believed to have seen an £8 million bid rejected, and the boss acknowledges that "every player has a price"
Hull City and Celtic are thought to be leading the chase for the Scotland international, with reports claiming Steve Bruce's side have seen an £8 million bid rejected.
Poyet is desperate to keep Fletcher as Sunderland battle against relegation, but the manager remains realistic and concedes that any member of his squad might leave if a big bid is submitted.
"I'm not the type of person to say 'no-one is for sale' and then we sell one," he told reporters. "Why? Because every single player has a price.
"That is the truth. If someone comes with a crazy offer for a player he will go. I'm not talking about Fletcher, I'm talking about every player.
"I've got no issues with Steven, that's why he's playing. If I had issues I wouldn't be playing him. We need to use the squad because of the quantity of games.
"I don't take anything personal with any player, sometimes they get it wrong.
"If they don't play, sometimes it can be a tactical reason and sometimes we don't explain it because if you did that every time you would not stop calling players.
"The idea is we try to get the best out of them. That is our job."