The Northern Ireland international spent last season on loan at The Den, making 33 appearances as Gary Rowett’s side threatened to qualify for the end-of-season play-offs.
Arsenal are understood to be receptive to that idea, with the youngster’s contract set to expire in two summer’s time, and may look to cash in this summer.
The Blades have looked at Ballard previously, as have a host of their Championship rivals. United have a significant bid on the table for a player this summer, with central defence identified as a priority position for boss Paul Heckingbottom.
First-choice centre-half Chris Basham recently signed a two-year contract extension, but will turn 34 next month and Heckingbottom is keen to ensure that successors for his most important players are in place before they move on or retire.
Ballard is a senior Northern Ireland international, and Arsenal would likely insert some sort of buy-back or first-option clause into any deal that saw him leave the Emirates.
Millwall boss Rowett revealed recently that his side have two bids currently in for players that would exceed their record signing – ironically the £1.5m they paid United for Ryan Leonard.
Rowett must also decide whether to consolidate his interest in Oliver Burke, the United striker who spent last season on loan at The Den. He will be allowed to leave Bramall Lane this summer if a suitable offer is made – but, with his United contract not set to expire until next summer, he is expected to report back for pre-season with United if a move elsewhere has not materialised.
“What I would say is the club are prepared to put some good offers out,” Rowett told the South London Press.
“We’ve put two bids at the moment that would probably be bigger than our record signing. It shows where we are. What we don’t want to do is not use that money wisely because it is a lot of money.”