The 31-year-old has been a rumoured target for Barcelona this summer alongside his Chelsea teammate Cesar Azpilicueta.
While Azpilicueta is expected to remain at Stamford Bridge, the signing of Marc Cucurella from Brighton & Hove Albion has opened the door for Alonso's departure.
According to the Daily Mail, Alonso has already said his goodbyes to the staff at Chelsea's Cobham training complex ahead of the move to Barcelona, which could be completed this weekend.
The Spaniard - who has already agreed personal terms with the La Liga club - is expected to sign a two-year contract at Camp Nou.
Although the transfer for Alonso is imminent, Barcelona may have to sell players before they can register the left-back after La Liga recently rejected their attempts to register their summer signings. body check tags ::