The 29-year-old spent seven years with the Midlands outfit before being sold to Fulham in a shock move in 2015, but rejoined Paul Lambert's side on a season-long loan in August.
During his second spell with Wolves, Stearman has surpassed the 250-appearances milestone for the club and is now setting his sights on matching teammate Dave Edwards's tally of 300.
"That would be great," he told the Express & Star. "I am playing now to try and extend my stay at Wolves. It has almost become like a trial period for me now.
"I have got to prove myself every day in training and if I get a chance, make sure I take it and show I deserve a place at this club. I have done it 250-odd times already and I want to continue to add to that.
"All I can do is play with my heart on my sleeve, play well, and do the most that I can to try and get a new deal – we will see."
Stearman recently found himself on the sidelines for nine straight games in the Championship but earned a recall to the starting XI on Easter Monday as the side claimed a surprise 1-0 victory at Leeds United.