The former-Anfield star remains a fan favourite at Liverpool, and with his Madrid contract set to expire at the end of the season, he's been linked with a return to the Premier League.
Currently on the sidelines with a broken foot, Alonso is yet to agree terms over an extension and recent reports claim Bernabeu chiefs are planning for life after the 31-year-old's departure by targeting Chelsea midfielder Ramires.
The La Liga giants also splashed out €39m on Spanish under-21 star Asier Illarramendi from Real Sociedad over the summer.
The report claims Madrid are willing to sell the ex-Liverpool star for a small fee in the January window. The alternative could see Alonso leave the club on a free transfer at the end of the season.
Real Madrid's reported interest in Ramires opens up the possibility of a cash-plus-player deal for Alonso from the Stamford Bridge hierarchy.
The World Cup-winning midfielder has been absent through injury this season, and Luka Modric has flourished in his place under new boss Carlo Ancelotti.
Liverpool remains a special place for the Spain international - he won the Champions League with the club in 2005 - and developed an excellent understanding with club captain Steven Gerrard.
But Chelsea have space in their squad for another central midfielder, following the cruciate ligament injury suffered by Marco van Ginkel last month.