Higuain scored 38 goals across all competitions during his one season under Sarri at Napoli and is a ideal fit for the manager's attacking style of football.
Higuain had his most successful season under Sarri, breaking the Serie A goalscoring record with 36 goals in the 2015/16 campaign.
However, the deal remains complicated with AC Milan remaining reluctant to terminate their existing loan contract with the Argentine and this could shift the Blues' interest elsewhere.
Vardy has scored seven goals so far in the Premier League and is one of the options that the Blues are looking at.
Higuain previously spent six years at Real Madrid after starting his career at River Plate in Argentina.
"It is hard to manage a striker when he doesn't score", said Milan sporting director Leonardo.
"He had a tough moment, he has to put it behind him and get to work", said Leonardo. Brazilian Leonardo added: "There's no point following rumours and gossip. Seeing as he is here, he needs to get down and actually do something for this team".