The 19-year-old has attracted the interest of Blades boss Neil Warnock and it is thought the Bramall Lane club have tabled a bid to The Bantams' administrators for the youngster.
However, The Black Cats look to have also entered the race for the defender, who is still under contract at Valley Parade until 2006.
With Bradford currently in administration, Francis looks set to follow the path of former team-mate Andy Gray and leave the cash-strapped West Yorkshire club.
"Because of the financial constraints here, we would have to consider any reasonable offer," Bantams boss Bryan Robson told the Sheffield Star.
Meanwhile, The Blades will be without striker Ashley Ward for at least four weeks with knee ligament damage.
There are fears that the former Bradford hit-man could miss the rest of the season with the problem, but he does not need an operation.
In other news, Sheffield United's reserve winger Ashley Sestanovich has not ruled out the chance of taking an international call-up with Concacaf nation Grenada.
The midfielder, who spent time on loan with Conference club Scarborough this season, did not accept his first invitation from the birth country of his father for last month's World Cup qualifier against Guyana.
"I haven't ruled it out but I don't want to jump straight into the first international call-up," Sestanovich told the club's official website.
"I understand that it may be my last but I'm still young and I want to see how things turn out.
"I spoke to the coach from Grenada and I told him what the situation was and he understood my point of view - but who knows what will happen in the future!"
Grenada defeated Guyana 5-0 in the first leg of their qualifying tie, with the second leg to be played on Sunday.
The winner will play Concacaf powerhouse USA over two legs in June.
