New Los Blancos bossJulen Lopetegui has failed to impress since taking charge in the summer, already losing two of his first eight La Liga matches and winning just four.
Real chiefs are prepared to pull the plug if results do not improve soon.
And Corriere dello Sport claims they have called Conte to check his availability.
The Italian tactician was replaced at Chelsea by Maurizio Sarri at the end of last season despite winning the FA Cup.
Conte fell out with the board after not getting the transfers he wanted in the wake of 2017’s Premier League title victory.
And although the former Juventus gaffer is still fighting for a £9million pay-off, he could soon find himself in the Bernabeu hot seat.
Conte has also been linked with Manchester United as a replacement for Jose Mourinho – who returns to his former club this weekend with his job under threat.
It’s been claimed that Conte’s Chelsea compensation would be reduced if he joins an English club before the end of the season.
But that would not be case if he moves abroad, which could make Real the more attractive prospect.
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