Despite beating Real Madrid, Liverpool and PSG to a deal for Lille defender Leny Yoro, United remain interested in signing England international Branthwaite.
Centre-backs Raphael Varane and Willy Kambwala have both left Old Trafford this summer, while Manchester United are open to offers for Harry Maguire and Victor Lindelof.
That has led Erik ten Hag to target another centre-back signing following the addition of French teenager Yoro, with his former Ajax player Matthijs de Ligt – currently at Bayern Munich – another option.
Manchester United have already made two unsuccessful bids for Branthwaite, who has made 54 appearances for Everton and was a key player in Sean Dyche’s squad last season.
The Red Devils were considering making a third offer to Everton but the Toffees have made it clear Branthwaite will not be leaving this summer, according to The Athletic.
Everton could yet be persuaded to soften their stance but only if a considerably improved offer is presented, with Goodison Park chiefs valuing the 22-year-old at around £75m.
Branthwaite was selected in Gareth Southgate’s provisional squad for Euro 2024 last month but then found himself cut from the final 26-man party.
Meanwhile, Manchester United confirmed on Saturday that new signing Yoro would wear the No. 15 shirt following his arrival from Ligue 1.
The Frenchman could make his first outing for the club on Saturday when Ten Hag’s side face Scottish giants Rangers in a pre-season friendly at Murrayfield.
‘Signing for a club with the stature and ambition of Manchester United so early in my career is an incredible honour,” Yoro said after signing a five-year deal at Old Trafford.
‘Since my first conversations with the club, they set out a clear plan for how I can develop in Manchester as part of this exciting project, and showed a lot of care for me and my family.
‘I know about the history of young players at Manchester United and feel it can be the perfect place to reach my potential and achieve my ambitions, together with my new team-mates. I cannot wait to get started.’
United sporting director Dan Ashworth added: ‘Leny is one of the most exciting young defenders in world football; he possesses every attribute needed to develop into a top-class centre-back.’
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