Aston Villa and Sevilla are already also known to be interested in the Brentford striker, who scored 28 goals in all competitions last season.
However, it is the Clarets who are ready to make a move with an opening £15m bid for Maupay. It is believed the Bees are holding out for closer to £20m.
This will come as a blow to the Blades, who have made Maupay one of their top targets. As the Sheffield Star reports, signing at least one new forward is a priority for manager Chris Wilder following his side’s promotion to the Premier League.
There are other options on Wilder’s wish list, though. Swansea City’s Oli McBurnie is another he is keen on, while Middlesbrough top scorer Britt Assombalonga has also been linked.
United are also understood to be keen on Jay Rodriguez. The Telegraph claims Rodriguez has a £5m release clause written into his West Bromwich Albion contract.
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Why Burnley and Blades want Neal Maupay
The 22-year-old has been in superb form since being brought to English football in the summer of 2017. Maupay cost just £1.6m – according to The Sun – when he joined from Saint-Etienne.
That first season at Griffin Park the Frenchman netted 13 times and now has 41 goals in 95 appearances for the Greater London team.
Yet Maupay has made no secret of the fact that he wants to play in England’s top flight. The attacker told the Independent that he would also be open to a reunion with former manager Dean Smith at Villa.
“If you’re in England, you want to play in the Premier League. That’s obvious. So one day I’d like to play in the Premier League.
“I have a really, really good relationship with Dean. So obviously if one day he calls me and says ‘Neal, I need you in my team’ I would consider it. But at this moment I can’t be focused on other things than Brentford.
“Obviously, I really liked working for him, so if one day he wants to bring me to Villa or wherever I would listen to him because he has done a lot of good things for me.”