Steele, a hero for the Tykes last season when he helped them reach the semi-finals of the FA Cup, has made only seven appearances this time around following the return to fitness of German goalkeeper Heinz Muller.
Davey said: "Players always want to be in the team. Luke Steele is out of contract in the summer and we want to keep him here.
"It is not going to be about money - it is all about whether Luke wants to play first team football and be a number one.
"That is something I cannot offer him at the moment. The unfortunate thing for Luke is that he has a 6ft 7in German keeper in front of him, who I rate as one of the best in the Championship.
"Luke is also right up there with the best in this division. We will sit down with him in the summer, but it will all be about Luke's ambition. We have a few players up in the summer, but the main thing on our mind is staying in the Championship."