They would want around €40million (£34m) to sell him in the next transfer window.
Everton have offered James Rodriguez a four-year deal to join them in the summer
Rodriguez has been made available for transfer for Real after a tough season for them
That has alerted a number of Premier League sides, according to Spanish outlet Mundo Deportivo.
Arsenal, Chelsea and Wolves are all eyeing the Colombia international as they look to improve their squads ahead of next season.
But Everton are thought to be the most keen on Rodriguez – with manager Carlo Ancelotti desperate to be reunited with him.
Carlo Ancelotti managed him at Real and Bayern Munich and wants another reunion
Ancelotti managed the 28-year-old at Real and took him to Bayern Munich on loan while he was in charge there.
He also tried to sign him at the start of the current campaign while he was Napoli manager.
The Italian is now willing to commit to a longer-term deal for Rodriguez and sign him on a permanent basis, offering a four-year deal, according to the report.
Rodriguez is thought to be keen on the move as it is the Copa America next year and he wants to join a team that will guarantee him minutes.