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Spaniard Isco is out of favour under Zinedine Zidane at the Bernabeu and will be allowed to leave in January.
According to The Mirror, any move will initially be on loan, with an agreement to make the deal permanent for around £18m next summer.
Arsenal, Juventus and Sevilla are also thought to be interested, but Isco is said to be keen on reuniting with Ancelotti and Rodriguez at Goodison Park.
Isco was Ancelotti's first signing as Madrid boss back in 2013 when the Italian snapped him up for Malaga for around £27m. Isco has gone on to make more than 200 appearances for Madrid, where he starred alongside Rodriguez.
During his time at Madrid, Isco has landed a host of honours, including two La Liga titles and four Champions League trophies.
However, the forward's relationship with Zidane has soured and he was allegedly caught on camera complaining about the Madrid boss ahead of last week's El Classico at the Nou Camp.
Isco has also been impressed by Rodriguez' form under Ancelotti at early Premier League leaders Everton.
A move to Merseyside could also boost his flagging career ahead of next summer's Euros.
Isco has started just twice for Madrid this season and was substituted in both games, being hauled off at half-time in the recent shock defeat to Cadiz.
It was reported that teammates hit out at Isco and Marcelo after that loss, but Zidane was quick to defend the pair.
"We're all in the same boat here and criticism makes us all stronger," Zidane said.
"Knowing where we're at and the situation, there is criticism, even more so after the game the other day but all we can and must do is get back to work."
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