Modric was crucial as Real captured a fourth Champions League title in five years at the end of last season and was in inspired form as he steered Croatia to their first ever World Cup final and won the Golden Ball as the tournament's best player.
The 4-2 defeat at the hands of France proved to be a game too far, but Modric is still arguably a genuine contender to win the 2018 Ballon d'Or later this year and finally break the longstanding Cristiano Ronaldo/Lionel Messi duopoly that has existed since 2008.
That makes the claim from Diario Gol (DG) all the more hard to swallow as it is alleged that Real president Florentino Perez sees soon to be 33-year-old Modric in a similar light to Andres Iniesta, who was recently allowed to leave Barcelona to enjoy the twilight of his career in Japan.
The story suggests that Perez believes that Modric is 'running out of batteries' and is looking to shake things up for the future. It is further claimed that Casemiro could be a casualty of a rumoured overhaul, although only one and not both midfielders would leave this summer.
DG has tipped Modric's much younger international teammate Mateo Kovacic to become increasingly involved for Real alongside midfield mainstay Toni Kroos.
Modric would certainly provide experience and knowhow for an exciting Liverpool team that reached the Champions League final last season, while Chelsea first tried to sign him in 2011 back when he was still a Tottenham player.
Exactly how much truth there is to the claims remains to be seen, but this is certainly one to keep an eye on in what remains of the summer transfer window.
If they do bid farewell to Modric, might Real regret it in the same way that AC Milan did when they let a 'past it' Andrea Pirlo move on in 2011?