Sources have told ESPN FC that Barcelona have also been offered the chance to loan Morata, but he is not their main target.
Sarri asked his Chelsea board to sign Higuain last summer but they were concerned by Juventus' £32million valuation of the 31-year-old.
Higuain is now on loan to AC Milan from Juventus, but the Rossoneri are reportedly ready and willing to let the 31-year-old end his spell early as they are struggling to pay his hefty wages.
The move is a complicated one given the loan agreement between the two Serie A clubs, but Chelsea have been working on a deal for a number of weeks.
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However, the article claims that Chelsea FC are willing to pay both as they look to bring the forward to Stamford Bridge this month.
Information from ESPN FC's Chelsea correspondent Liam Twomey and Spain correspondent Eduardo Fernandez-Abascal was used in this report.
The objective of a temporary deal is to allow him to rebuild his value elsewhere, but sources have told ESPN FC that Chelsea want any loan club to cover Morata's salary in full until the end of the season and he will not be allowed to depart until a replacement striker is secured.
Higuain scored 38 goals across all competitions during his one season under Sarri at Napoli and is a flawless fit for the manager's attacking style of football.