Bruce revealed early discussions have already taken place to keep him at the KC Stadium.
He 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."