Former player Beresford grew up in Sheffield and is a lifelong United supporter, but never played for either club in a professional career which spanned three decades.
Hirst has found himself excluded by Sheffield Wednesday at all levels this campaign amid an ongoing contract dispute.
His current deal expires in the summer and several Premier League sides are said to be keen on signing him given his exploits for England's youth teams.
But Beresford - who is friends with Hirst's father David, a former teammate of his, albeit briefly, at Barnsley - has described the Owls' stance as "idiotic" and suggested they stand to receive as little as "£500-600,000" if the 18-year-old leaves in 2018.
Comparing Hirst's situation with that of his former England Under-20 teammate David Brooks, who has played 18 times for Sheffield United this season, the 51-year-old said: "Talk about two contrasts. You’ve got a lad at Sheffield United who’s going, 'right, I’ve got a club that wants me,' and you’ve got a lad on the other side who’s going, 'you don’t want me'.
"So Sheffield United could have two players… I didn’t say which player, I’m just saying you never know what might happen.
"I’m turning into [Beresford's former Newcastle United manager, Kevin] Keegan now - I’d love it if that happened."
Could Hirst quit Sheffield Wednesday for Sheffield United?