Fletcher, who has made 342 appearances for the Red Devils, has only six months left on his contract at Old Trafford and is struggling to establish himself under new boss Louis van Gaal.
Tony Pulis has admitted West Brom are in talks to sign the 30-year-old Scot and Allardyce hopes Fletcher will make a final decision soon.
"We've had no permission to speak to Darren Fletcher," Allardyce said.
"He's got quite a few clubs interested in him so when he makes his mind up everyone will know.
"I don't know what the timeline is
If any of the other packages offered to him are accepted then we would accept that.
"Or if they hadn't made their mind up or were negotiating somewhere else that would be it
We can't wait forever.
"I always think at this stage of the window, if you do get something nailed on you have to take it because you might end up with nothing if you don't."
Source : PA
Source: PA