The playmaker's future remains somewhat uncertain at the Bernabeu with no new contract agreed yet.
Isco is in negotiations over an improved deal, but other top clubs are said to be keeping tabs.
With the Spain international's current contract expiring in 2018, Manchester United, Chelsea, Manchester City and Paris Saint-Germain are lurking.
And Barcelona are also interested in swooping from their La Liga rivals.
Real Madrid want Isco to stay at the club despite not being a key player
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Lionel Messi is keen on seeing Isco switch Madrid for the Nou Camp
Lionel Messi is keen on seeing Isco switch Madrid for the Nou Camp.
But according to Spanish outlet Diario Gol, Perez is fighting back after Messi and Barca's pushes to sign the 24-year-old.
Madrid deem Barca's approach controversial, and it is claimed if the Catalan club are playing over Isco's future, Perez can play Messi in return.
The Madrid chief is pulling all the strings to make Isco more expensive to other clubs with a renewal at the club.
As a result, Messi has been left in a situation where he cannot demand top signings such as Isco while requesting a significant pay increase himself too.
The Argentina international wants the best team at his side, but Madrid are looking to price Barca out of taking their creative midfielder.
Reports least week claimed Barca have held secret talks with Isco, although he could yet remain in Zinedine Zidane's team.