The Blades boss, who snapped up midfielder Andy Gray from The Bantams recently and former Charlton Athletic and Barnsley goalkeeper Sasa Ilic from under the noses of the Valley Parade club, is eyeing a move for young defender Simon Francis.
Warnock admitted that Francis is one of a number of transfer targets that he is considering for strengthening his squad, as the Bramall Lane club aim for promotion from Division One.
The 19-year-old is in the first season of a three-year deal with the cash-strapped West Yorkshire outfit, having put pen-to-paper on his first professional deal with Bradford last May.
"We've looked at him, as we have many players," Warnock told the club's official website.
"Obviously someone has let it out of the bag that we have monitored his progress.
"I'm always looking to strengthen the squad, over the past few weeks we have been left with just four defenders so we need more cover."
Meanwhile, The Blades have announced that midfielder Stephen Jagielka has not joined Conference club Scarborough on loan.
The former Shrewsbury Town man, who is brother of Blades midfielder Phil, cannot join The Seadogs as they have borrowed two players in Ashley Sestanovich and Colin Cryan this season.
Conference clubs cannot take more than two players on loan from any one club in a season.
In other news, two of Sheffield United's young goalkeepers have taken loan spells at non-league sides.
Canadian youth international Tom Lindley has joined Gainsborough Trinity while American custodian Andrew Britton has joined Bradford Park Avenue on loan.
