Pulis is desperately trying to bring in a new keeper after Neil Cutler and Ed de Goey picked up injuries in last weekend's win over Watford.
It is not known how long the pair may be sidelined for, but Pulis is keen to bring in experienced cover as both men recover.
"Our goalkeeping situation is a real cause for concern," said Pulis.
"We are very keen on Crossley but he is still a Fulham player."
Crossley has already enjoyed two loan spells at Stoke over the last two years and he could be keen on a return to The Britannia Stadium in a bid to get first team action.
The Welsh international has made just two appearances this season with Edwin van der Sar the established number one and the club could be willing to let him go.
