Rumours were rife last month of a possible return for the Spanish international, who enjoyed a five-year stint at Anfield after being signed by Rafa Benitez in 2004. In that time he won the Champions League and FA cup in consecutive seasons, establishing himself as a key player in the process.
And it is thought a return to Merseyside may now appeal, with his contract at current club Real Madrid set to expire at the end of the season.
The speculation comes as Liverpool are also linked with fellow Spaniard Koke of Atletico Madrid, adding to the speculation that Reds manager Brendan Rodgers wants to bolster his slim central midfield options.
Though Koke would fit the club’s mould of adding young players to the ranks, the 31 year-old Alonso could prove an exception to the rule and it is thought that his current owners may be willing to sell to avoid losing him for free at the end of the season.
The Anfield outfit may face competition for Alonso’s signature, however, with Jose Mourinho’s Chelsea also being linked with the player.
Meanwhile, rumours are also circulating of a Madrid move for the Blues Brazilian midfielder Ramires, making Alonso’s future at the Bernabéu look all-the-more uncertain.