Simpson suffered a hamstring strain in the replay with Burnley and was ruled out of the home league defeat against Newcastle last weekend.
Tony Mowbray is hoping the current poor weather will improve to allow Simpson to be put through his paces at the club's training ground.
"I would hope Jay would be back for the Fulham game, but there are no guarantees," he said.
"If depends if we can get out on the training pitches. If we can get him jogging and running, he'll be pretty close for Fulham."