The 20-year-old has not featured for the Blades in any competitive sense during the 2023-24 campaign due to a mixture of injury and illness.
Jebbison was a fringe player as Paul Heckingbottom's side earned automatic promotion from the Championship last season, enjoying his maiden campaign in the first-team squad as a youngster.
The England Under-20 international appeared in 16 second-tier matches as United finished second behind Vincent Kompany's Burnley, scoring one goal.
Speaking to The Sheffield Star following Sheffield United's 2-2 draw at the Vitality Stadium against Bournemouth over the weekend, Chris Wilder stated that Jebbison wants to remain at the Yorkshire club.
"That was put on the backburner because of his injury but there has been real positive talks between Steve Bettis, his representative, his family and me - I have been involved in that as well," said Wilder when asked about ongoing contract talks between the Blades and Jebbison.
"I know the boy wants to stop, he has never given any other indication to me and his family hasn't said that he wants to move away. And we'll be delighted if we can tie another of our promising youngsters up."
As alluded to, Jebbison's current deal at Bramall Lane expires at the conclusion of the 2023-24 campaign, and the club do not hold an option to extend those terms.
Therefore, the 20-year-old and the Blades must agree on a fresh contract or the attacker will be eligible to depart on a free transfer ahead of the 2024-25 season.
Wilder's comments are contradictory to reports that emerged last week, with journalist Alan Nixon claiming that Jebbison would be leaving the club in the summer.
The report also states that fellow attacker Oli McBurnie will move onto pastures new in the summer, with the Scotland international not currently in discussions over a new deal.
United are also set to lose Cameron Archer at the end of the season, with Aston Villa supposedly obligated to re-sign the forward should the Blades fail to avoid the drop.
With Ben Brereton Diaz expected to return to La Liga side Villarreal at the conclusion of his loan spell, the Blades only have Rhian Brewster and Will Osula as contracted strikers heading into next term.
Wilder is hopeful that Jebbison will be able to make his maiden appearance of the season when Sheffield United host Fulham on March 30, following the calendar year's first international break.