Recall that Conte was last week among the two coaches who were shortlisted for Madrid job.
Conte is currently without a team since leaving the Blues in the summer.
Lopetegui, on the other hand, is under intense pressure at the Los Blancos just four months after taking over from former Madrid boss, Zinedine Zidane.
Madrid suffered a 1-0 shock defeat to Alaves on Saturday evening in the La Liga to make it the fourth matches without a win in all competitions.
The Los Blancos also lost to Sevilla and CSKA Moscow and played a draw with Atletico Madrid.
Lopetegui’s side will take on Levante in their next La Liga fixture on October 20.
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