The future of the 22-year-old remains far from certain with United and Bayern Munich both closely linked with the midfielder, who reportedly wants to leave the Camp Nou.
The player is due to return to pre-season training after playing a starring role in Spain's European Under-21 Championship success.
Reports claim that Barca sporting director Andoni Zubizarreta met with the player's father and agent - former Brazilian international Mazinho - on Thursday, and told him the club want a decision on Alcantara's future in 10 days.
When approached by Sky Sports, a Barcelona source would only say: "We still have not received any formal offer for the player."
It is claimed Barcelona are not looking to negotiate Alcantara's sale with anyone, but he is widely reported to have a buy-out clause of just over £15million so they would be unable to prevent him leaving if this figure was met.
Reports suggest that Alcantara does not believe he will be able to claim a regular starting spot ahead of the likes of Xavi, Andres Iniesta and Cesc Fabregas, which is why he is keen to look for regular first-team action elsewhere.
Last season Alcantara started just 15 league games for Barca, and of those he was taken off seven times.