But what chance to the Whites actually stand of landing the England Under-19 star?
HITC Sport takes a look:
Why would he leave Sheffield Wednesday?
Hirst's departure, whether at the end of his contract or sooner, is looking increasingly inevitable. He may be the son of Hillsborough favourite, David, and a lifelong Owl himself, but his failure to sign a new contract has seen him banished from every age group this campaign - his only football coming for England's Under-19s. Even if that issue were to be resolved, Hirst would need to beat off competition from a plethora of strikers - Gary Hooper, Steven Fletcher, Jordan Rhodes, Lucas Joao and Fernando Forestieri - before making the first team.
Why would he choose Leeds?
Leeds' striking department isn't nearly as congested as Wednesday's, while the Whites have always had an excellent record of promoting young talent, making regular opportunities far more likely than at Hillsborough. Earlier this season, Hirst's father was overheard saying he'd "heard good things about Leeds", but that was when they were top of the table. They're 10th now - level on points with Wednesday.
What obstacles might Leeds face?
Leicester City are also being linked, while several of their Premier League rivals, including Everton and Arsenal, are said to have shown an interest previously. A top flight move is bound to hold significant appeal to Hirst, even if it means fewer opportunities - and literally anything would be an improvement at this present moment. Money could be the killer for Leeds, however, with Wednesday's wage budget believed to be far higher than that of their Yorkshire rivals. And if they're unwilling to meet Hirst's demands, what hope does that leave Leeds?
Our verdict: The Premier League beckons for Hirst. In which case, Leeds, you've got six months to get there - and hope he doesn't beat you to it.