The Real Madrid star has 18 months still to run on his contract at the Santiago Bernabeu, but as talks over a new deal continue to stall, the 31-year-old has revealed he would welcome a move back to England.
"I've no idea what will happen," he told reporters in Spain. "I have not decided on my future.
"I will only stay at Real Madrid if I can offer the same level on the pitch as I can now and we will see what happens in the next few months."
Alonso spent five successful years at Anfield, winning the FA Cup and Champions League during his time on Merseyside under Rafael Benitez, before leaving Liverpool for Real Madrid in 2009.
The Spain international continued his trophy haul back in his homeland, with last season's La Liga title following the club's Copa del Rey triumph a year earlier, with the help of manager Jose Mourinho.
He was named the best midfielder in the Primera Division in 2011/12, ahead of Barcelona duo Xavi Hernandez and Andres Iniesta, which is no mean feat considering the contributions of both his La Roja team-mates.
But, a Premier League comeback remains a possibility for Alonso, who is still a huge fans' favourite at Liverpool, and would be welcomed back with open arms should Brendan Rodgers try to add him to his squad.
"There is always a chance I could go back to the Premier League as I always enjoyed good times there," he added.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms