Conte’s brother, Daniele, was asked about the situation by Spanish radio station Cadena Ser on Thursday and said that, while Real are a “great club”, there has not yet been contact with them.
“Antonio is on holiday at the moment,” he said. “He hasn’t received any phone call from Real. We can definitely say it’s a great club, but for now there’s been no contact.”
The former Italy manager rejected the chance to join RealMadrid last summer in order to take a break from football following his departure from Stamford Bridge.
On Wednesday, Chelsea were not commenting on reports that they would be owed as much as £9.5m in compensation should Conte take a job in the coming weeks and months.
Lopetegui, meanwhile, was sacked from the Spain job after agreeing to take over from Zinedine Zidane in the build-up to their World Cup campaign, subsequently taking over at LaLiga champions in June.
But he already finds himself under pressure after winning just six of his 13 games in charge.
