The Barcelona star impressed for the Spanish giants last time out.
Roberto started 39 games in all competitions last season, netting one goal and chipping in with six assists.
The Spain international, 25, has been linked with a Nou Camp exit in recent weeks, with Chelsea said to be keen on the midfielder.
However, according to Spanish outlet Diario Gol, United are also in the hunt for Roberto.
They say the Barca ace is a big admirer of Red Devils boss Jose Mourinho, who has been in contact with Roberto.
Diario Gol add that Roberto is open to joining United this summer.
However, the midfielder wants to know if he will get regular game time next season under Ernesto Valverde before making his decision.
Diario Gol say he will not hesitate to quit the Nou Camp for United if he cannot be guaranteed first-team football at Barca.
Roberto would become United's fourth summer signing if he makes the switch to Old Trafford.
The Barca ace would follow Romelu Lukaku, Nemanja Matic and Victor Lindelof to the Red Devils.
