Madine is currently on loan at Bramall Lane from Cardiff, but Blades manager Chris Wilder is keen to keep hold of the 28-year-old.
The forward has scored three goals for United since arriving in the January transfer window. He has also played a big part in the club securing automatic promotion to the Premier League.
Madine has previously admitted that he wants to stay in South Yorkshire beyond his current temporary spell as well.
“This feels like home to me now. I’d be devastated if I had to move on from here at the end of the season. I’d love to stay for as long as the manager wants me and hopefully that’s beyond the summer,” he told the Sheffield Star earlier this month.
“These lads are a special bunch, working daily with this manager and his staff is something I’ve relished. I don’t want to be disrespectful to Cardiff City but it’s a long way from home and it’s never really happened for me there.
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“I’m settled here, I’m content and happy. I’ve proved I play my best football when I’m happy and I couldn’t be happier than I am at Sheffield United.”
How much will Madine cost?
The attacker may want a permanent move to the Blades, but he’s still under contract in the Welsh capital until 2021.
Madine only joined the Bluebirds from Bolton Wanderers in a £6m deal in January 2018. He has played 19 times for them since but has failed to score a single goal.
It is likely that Cardiff would want to recoup a large proportion of the fee they paid for Madine. Whether Wilder and United view that as affordable remains to be seen.
However, they will need more options upfront. Currently Billy Sharp and David McGoldrick are the only players in the role under contract for next season.