West Ham United have been linked with the Manchester United midfielder, with several clubs said to be in the running. Allardyce was speaking at his pre-match press conference ahead of the FA Cup tie against Bristol City.
Fletcher has been linked with a move away from Old Trafford with several Premier League clubs said to be interested in him, including West Bromwich Albion.
At his pre-match press conference ahead of the FA Cup fourth round tie with Bristol City, Allardyce said: "Darren Fletcher has got several clubs interested in him, so it is up to him where he wants to go."
The Hammers boss says only two players miss out on the game against Bristol City with forward Diafra Sakho and defender James Collins both missing out.
Allardyce added: "Bristol City are doing well at the moment in League One. Several Premier League teams have struggled against lower league opposition.
"It's all about the attitude of our players. They need to rise to the occasion.
"I don't have a problem playing my full strength team as we've got a full week until our next league game.
"We put a lot of energy into the Everton tie, over two games, so we don't want that to be in vain. We want to win on Sunday."
The cup win over Everton represented the first FA Cup tie won by Allardyce during his reign at the Boleyn Ground, and with a favourable tie this weekend, he will be hoping the side can push on and have a productive run in the competition.
He will have looked at sides in recent years that have managed to get to the final like Wigan Athletic and Hull City, and will see his side are in better health than those two sides were at the start of their cup run, and believe his side have a chance of getting to the latter stages of the competition.