City have joined St Johnstone and Livingston in pursuit of the 28-year-old who has featured only sporadically at Tynecastle Park this season. Hearts are open to a loan or permanent transfer this month but Walker will be allowed to decide his own future.
Derek Adams, manager at Valley Parade, is an admirer of the player and has made a move to take him south on an initial loan deal. Bradford are currently 12th in League Two and have aspirations of reaching the play-offs to aim for promotion.
Other teams are also monitoring Walker. His Hearts contract expires at the end of the season and an extension is not on the table as things stand. He wants to play more regularly in Gorgie but is further down the queue for first-team places and must now decide whether to move on during the current transfer window.
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He has made just four league appearances, all as a substitute, to date this term but did manage to score the winning goal against Dundee at Dens Park last month.
Walker previously spent 18 months in England after leaving Hearts to join Wigan Athletic for a reported £300,000 in January 2018. He returned to Tynecastle on a free transfer in summer 2019, signing a three-year deal.
As that agreement nears an end, he is now faced with the prospect of continuing his career elsewhere. Hearts will happily let him stay for the second half of the season but cannot guarantee him regular game time.