Lopetegui is under increasing pressure, after seeing a winless run stretched to five games with defeat at home to Levante on Saturday.
Jose Luis Morales and Roger Marti gave Levante a two-goal lead within 13 minutes of the game, to heap more pressure on the European champions.
Real had chances to score, but could only pull one back through Marcelo in the dying moments of the game.
It is their worst run since May 2009, when Juande Ramos was sacked.
Speculations in Spain claim Lopetegui will be fired imminently.
According to a report from Corriere dello Sport, Conte is on standby to step in at the Santiago Bernabeu, possibly before next weekend’s El Clasico against Barcelona.
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