Wickham, 19, who scored his first goal for the Owls in Saturday's 1-0 win at Leicester, is due to return to parent club Sunderland after making six appearances during his month-long youth loan at the club.
But Jones is keen to extend the England Under-21 international's stay at Hillsborough.
"I will sit down with the chairman, talk to Martin O'Neill up at Sunderland and see where we go from here," Jones said after his side had climbed four points clear of the relegation zone with victory at Leicester.
"He's a pleasure to work with, he wants to learn and I'm delighted for the lad that he has got his goal."
Wickham has said he is not sure where his short-term future lies, but that he had enjoyed his spell with the Owls.
Jones added: "Connor was superb in getting the goal, but they all were. They deserve all the plaudits they will get from this win."