The 27-year-old, who joined the club on loan in January, has played a key role in a run of form that has taken them to second position in the Championship table.
Stockdale is highly regarded at Fulham, but with Mark Schwarzer showing no signs of retirement, the English goalkeeper could be forced to look elsewhere for first-team football.
Bruce told the Hull Daily Mail: "I don't think it is set in stone, but it is something that has been discussed. There is certainly the possibility of a deal to be done if we were to get to the Premier League. That is where Stockdale wants to play and that is where we all want to play.
"He has played a big role from the minute he walked in through the door here. And he has still got a big part. He handles the situation well and that is where his experience comes in.
"It is important to have that position as a position of strength and that is what he gives us. You can count on one hand the number of mistakes he has made, so he has been very influential."
Stockdale has kept eight clean sheets in his last 19 games.