Adkins managed Sharp at Scunthorpe, Southampton and Reading, and reports last week claimed he had made an offer to sign him again after being confirmed as Nigel Clough’s successor at Bramall Lane.
However, the 50-year-old insists he needs to meet his new squad before deciding what players he needs to sign this summer.
“Sharpy is a Leeds United player at this point in time, simple as that,” Adkins told the Sheffield Star.
“We had him at Scunthorpe and sold him to United, then we took him to Southampton with us and brought him in on loan at Reading, too.
“But we’ve got to first get in there when the players come back, assess the personnel we already have at our disposal and then go from there.
“We also have to work under the restraints of the club.
“We have a lot of players under contract and we’ll have to give them the opportunities to keep moving forward.
“We’ll work with the owners because we all want the same thing, but we are mindful of the limitations of Financial Fair Play and SCMP. We will have to be wise in what we’re going.”