Chairman Dejphon Chansiri is urging striker George Hirst to quickly make his mind up on his Owls future.
Hirst is training with the first-team squad and playing in Under-23 matches again, having been frozen out at Hillsborough for much of the season over a long-running contract dispute. His present deal is due to run out in the summer.
The 19-year-old scored on his Wednesday return in the development squad’s 3-2 defeat at Leeds United in February and also featured in their home draw with Crewe Alexandra last week.
However, the Owls are refusing to allow Hirst to be considered for selection at senior level until his long-term future is resolved.
Speaking at the Steering Group Meeting on Friday night at Hillsborough, Chansiri revealed Hirst still has a contract offer on the table.
“It depends on him now and what he’s going to do,” he said. “I still hope that he will sign.”
Although Hirst has yet to commit himself to the club, Chansiri recently agreed to let him play for the U23s after holding productive talks with the player.
“I respect him because he asked me to play,” he said. “I’m happy to step back and let him play.
“Let’s see what happens. I can’t make a decision. I told him he has a big chance (here).”
Hirst, capped at England Under-19 level, plundered 40 goals for club and country last term. Wednesday have previously knocked back bids for him from Everton and Leicester City.
Another youngster who the Owls are still looking to tie down to a new contract is midfielder Sean Clare.
Chief executive Katrien Meire said: “We have made it clear we want to sign him. The contract offer is there so we wait on a decision. I hope we can finish that one.”