The 31-year-old Spain midfielder spent five years at Anfield before sealing a switch to the Bernabéu in 2009.
Alonso has 18 months left on his current contract with the La Liga outfit – and he admitted he would be open to a move back to the Premier League should he not extend his stay at Real Madrid.
“I have not decided on my future,” said Alonso. “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.
“There is always a chance I could go back to the Premier League as I always enjoyed good times there.”
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