Ex-Liverpool star Alonso, 31, has 18 months left on his contract but talks on a new deal have stalled and he fancies a move back to England.
Alonso said: "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.
"There is always a chance I could go back to the Premier League as I always enjoyed good times there."
Source: DSG