His 12-year stay in the Spanish capital may finish when his contract expires at the end of the season.
Modric’s agent previously hinted that the 38-year-old has already had offers from several other teams.
And there is speculation he could be the next big star to sign for a Saudi Arabian club.
Modric is supposedly open to moving to the Middle East if the offer is “suitable”.
Saudi sides are again expected to splash the cash this January.
But any deal for Modric will have to wait until the summer as Real Madrid want to keep him as cover in midfield.
A transfer to Saudi Arabia will see him follow down the same path as other Los Blancos heroes and Ballon d’Or winners Cristiano Ronaldo and Karim Benzema.
Modric has played 503 games for Real Madrid, winning three LaLiga titles and five Champions Leagues.
But he has started just six games this season after being pushed out the side by Jude Bellingham.
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And Modric does not want his career to slow down after helping Croatia move one step closer to Euro 2024 qualification with a 2-0 win over Latvia last night.
He previously said he no plans to hang up his national team boots.