The Scotland international has seen appearances limited at Old Trafford this season, with just four Premier League starts under Louis van Gaal in 2014-15.
Pulis revealed in a press conference on Thursday that West Brom had registered their interest in the player, but that the club were waiting for Fletcher to weigh up his options.
"He is talking to three or four clubs. We showed an interest and he'll make a decision and we'll wait and see," Pulis said.
The head coach, who took over from Alan Irvine on New Year's Day, said that West Brom were in talks with Wigan Athletic about a possible deal for Callum McManaman, before bemoaning the lack of time available to him in the January window.
He added: "It's the most difficult window I've had because I've not had time to get things in place."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
