Madrid have registered just one win in their last six matches and reports are suggesting that Lopetegui will be sacked if his side suffer defeat in their clash with Barcelona on Sunday.
Conte has been heavily linked with becoming Madrids next manager although his brother and agent Daniele claimed earlier this week that the Champions League holders have not made an approach.
Conte is due a £9 million payout after being sacked by Chelsea in the summer but the club have been haggling over the terms of his severance package.
But according to Sport Mediaset, Conte is a major step closer to becoming Madrids new boss after he reached a settlement with Chelsea on Friday.
Now Conte no longer has a contract with Chelsea, the Italian would be free to immediately take up a position at Madrid.
Sport Mediaset also report that Conte has won the resistance of the Madrid dressing room as Ramos has given the green light for the Italians arrival at the Santiago Bernabeu.
If Madrid lose at Camp Nou on Sunday it would put them seven points behind Barcelona after 10 games played.
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