The Manchester United and Chelsea target is out of contract at the end of the season, and he was linked with a free transfer return to the Premier League.
But Spanish news site Punto Pelota claims Alonso told a Manchester United official - a friend of the player who helped Alonso move to Liverpool - that he thinks he'll probably stay at Real Madrid after all.
The unnamed United representative reportedly asked Alonso about his availability - the Spain international would be free to discuss terms on a contract with foreign clubs from January onwards - but Alonso stated that he doesn't expect to leave.
The report stresses that the United official was not working in his capacity as an employee of the Premier League champions, but was instead asking as a friend of Alonso's.
A target for United and Chelsea in recent weeks, French newspaper Le 10 Sport suggests the Premier League duo will now have to explore other options heading into the January window.
The Spain international recently returned from an extended period on the sidelines following a fractured metatarsal, with speculation suggesting the arrival of Asier Illarramendi could make the 31-year-old Alonso surplus to requirements.
United are expected to be busy in the January transfer window, with Old Trafford boss David Moyes thought to be keen to strengthen after a difficult start to life as Sir Alex Ferguson's successor.
Likewise, Jose Mourinho has not had it all his own way in his new job, with the Blues boss publicly slamming his Chelsea side following their recent 2-0 defeat to Newcastle.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms