Earlier on Monday, League One club United announced they had "reluctantly accepted" a bid from Hull for the 21-year-old defender.
However, confusion then ensued as Hull claimed their "final offer" for Maguire had been rejected last Wednesday.
As such, the Premier League club's board will now meet with manager Steve Bruce to decide whether or not to pursue the prospective deal.
"Sheffield United rejected an offer from the club five days ago for defender Harry Maguire," read a statement on Hull's official website.
"This was the club's final offer and we have since entered into discussions with other transfer targets.
"In light of Sheffield United's statement this morning the board will meet with manager Steve Bruce this afternoon to determine whether we now wish to pursue the transfer after the South Yorkshire club's apparent U-turn."
In United's statement, released an hour and a half before Hull's counter statement, managing director Mal Brannigan said: "We made it clear that we wanted Harry to stay by offering him a new contract at the end of last season - unfortunately he and his representatives chose a different path.
"However, as he is under contract at Bramall Lane, we exercised our right to set our own valuation of him and after numerous bids which did not meet our expectations, Hull City increased their offer and we have reluctantly accepted."
Maguire, who has represented England at under-21 level, has become a regular at the heart of United's rearguard after breaking into the team at the end of the 2010-11 season.