Laurent Blanc and former Madrid players Guti and Michael Laudrup are other names believed to have been under consideration if Lopetegui is sacked.
Real Madrid are now on a five-game winless run in all competitions.
After making a bold team selection that included naming Bale, Toni Kroos and Benzema on the bench, another awful result here, coupled with an historically bad goalscoring streak, has him on the brink of the sack.
"They caught us with a goal when we were doing well".
"He tells us things very clearly". We need to change this dynamic. From there he was part of a Madrid defence that was wide open and regularly vulnerable to Levante's counter-attacks, the visitors having a third goal ruled out before the break.
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The ton was his 14th as India's ODI captain, edging him closer to Ricky Ponting's record 22 as Australian skipper. Up front we went to get wickets as that was the only way to put them under pressure.
Real had chances to score, but could only pull one back through Marcelo in the dying moments of the game.
Madrid struck the woodwork three times and had a goal by Diaz disallowed for offside in the final minutes.
It's no secret Lopetegui is virtually guaranteed to suffer the same fate if he doesn't turn things around soon - but it appears he may already be out of time.
The club, then, will not go down as the most incompetent finishers in Madrid history - but it is scant consolation as they once more tasted defeated in a 2-1 reverse.
The result left Madrid fifth and in danger of dropping further down by the end of the weekend's round.
According to FootballItalia, Conte is 'waiting in the wings, and cite a report from Spanish newspaper El Pais that he was contacted by the club on October 2nd, immediately after Madrid's loss to CSKA Moscow in the Champions League.