The former-Anfield midfielder has been a key player for Real Madrid and Spain since joining the reigning La Liga champions from Liverpool in the summer of 2009.
But reports in Spain claim that Alonso is yet to sign a new deal with Real Madrid. The Spain star is thought to be holding out until the future of Jose Mourinho is resolved in the summer.
Alonso's Madrid contract runs until the end of the 2013-14 season, and he's in no hurry to extend as uncertainly continues to surround the club.
Mourinho has been linked with a move away from the Bernabeu, with Chelsea and Paris St Germain both thought to be keen to lure him away from the Spanish capital.
The report claims Real Madrid are not entertaining the notion of selling Alonso, but Liverpool are hopeful that they can convince him to return to Anfield as his contract runs down.
The Premier League club have reportedly enquired about his availability in the past few months, and his reluctance to put pen to paper will only serve to encourage Liverpool in their pursuit.
The Reds have never really replaced the Spaniard, with Joe Allen brought in last summer to get the Merseyside club passing again. But in Brendan Rodgers' possession based system, Alonso could be a real asset.
The 31-year-old has won the Copa Del Rey and La Liga with Real Madrid, and his side progressed to the quarter-finals of the Champions League last week with a 3-2 aggregate victory over Manchester United.
Alonso won the Champions League with Liverpool back in 2005.