The Premier League side completed the signing of Harry Maguire on Monday but they could still add another centre-back before the transfer window closes on Thursday.
The Spanish outlet claim that Umtiti has received offers from both Manchester United and PSG as he plots his next move.
The Frenchman slipped behind Clement Lenglet in the Camp Nou pecking order last season, and is said to be considering his future.
Umtiti would be open to a move away from Barcelona, while the Catalan club are also willing to listen to offers.
United boss Ole Gunnar Solskjaer has hinted that his side will not have completed their business even after the purchase of Maguire, amid Umtiti’s continued links with Old Trafford.
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