Following a lacklustre Premier League campaign last term, United have been very busy in the summer's transfer window.
Sky Sports have picked up on something in the Spanish media vehicle, Don Balon and reporting that Roberto is subject to interest from two English Premier League clubs, Chelsea and Manchester United, and also the La Ligue club Monaco.
However, Roberto's future at the Nou Camp is now in serious doubt as he's expected to lose his place in new boss Ernesto Valverde's starting eleven following the arrival of Nelson Semedo from Benfica.
This has led to speculation that the Spanish worldwide will look for a move this summer in order to secure regular action ahead of the 2018 World Cup and a move to the Premier League has been mooted.
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Roberto has established himself as a key player within the Barcelona first team squad over the past few years, and can play in a number of positions.
Mundo Deportivo reported that United have made a bid for the Spain worldwide, while sources told ESPN FC last month that he was also a Chelsea target.
Mundo Deportivo add that Chelsea are also eyeing Roberto this summer.
Despite reports suggesting that the Catalan side are reluctant to let the player leave after the departure of Neymar, Mundo Deportivo states that United have submitted an offer which has been rejected by the club.