Wickham's initial one-month loan from Sunderland expires after Wednesday's clash with Leicester City on Saturday, and Jones has expressed his desire to keep hold of the 19-year-old striker.
"I would like to keep Connor definitely," the Shields Gazette quotes him as saying.
"I think he would like to stay. It will all depend on what Martin O'Neill feels about him.
"He has not played a lot of football over the last year and that eventually does catch up with you. I think the kid has got an abundance of ability."
Wickham has not scored in four appearances for Wednesday.