The Daily Mail is reporting that the Spanish giants are interested in appointing the Italian manager as their new boss after Zinedine Zidane stood down at the end of the season.
The same report says that Real Madrid have turned their attentions to Conte after Juventus boss Massimiliano Allegri turned down the job on Monday.
It is being claimed that Madrid view Conte as the only top level manager who is likely to be available this summer and they are prepared to makea move for the Chelsea FC boss.
Conte’s situation at Chelsea FC remains a constant source of speculation, with the Italian widely expected to leave Stamford Bridge this summer.
The Blues ended up in fifth place in the Premier League table last season as they missed out on qualification for next season’s Champions League.
The west London side did, though, manage to end the campaign on a high by beating Manchester United in the FA Cup final at Wembley last month.
Chelsea FC will be looking to break back into the top four next season.
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