The 31-year-old is in the penultimate year of his Real Madrid contract and while the club are keen to hang onto the player, Alonso himself is in no rush to sign an extension.
Real have tried to open talks with the midfielder about a new deal, but the Spanish international seems more than happy to keep his options open for the time being.
He would certainly be welcomed back at Anfield with fans and team-mates alike remembering his first spell with the Reds fondly as he played a key role in the club's Champions League success during his first season.
Alonso may be waiting to see if Jose Mourinho stays at Real beyond the end of this season before committing his future, but if the midfielder does become available, he won't have any shortage of takers.
Liverpool last week