According to Diario Gol, Morata is resigned to waving goodbye to fellow Chelsea ace Hazard at the end of the season.
And, knowing the Belgian would be a guaranteed starter in Madrid, he wants the Blues to rescue Asensio to stop him from being pushed to the fringes.
Morata and Asensio played together at Real during the 2016/17 campaign and are both poised to go to the World Cup with Spain this summer.
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Alvaro Morata expects Chelsea to lose Eden Hazard to Real Madrid at the end of the season
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Diario Gol claim Morata has already told Chelsea to go after his compatriot when they lose Hazard to Real.
And Asensio would apparently be keen on a move to west London to ensure his progress is not hampered.
Asensio has made just nine La Liga starts this term and he's aware opportunities would be even harder to come by if Zinedine Zidane snared Hazard.