The Leicester star, who has seven goals in the Premier League this season, is part of a three-man shortlist that also includes Higuain and Bournemouth striker Callum Wilson.
Wilson, 26, has scored nine league goals this season and has been linked with a move to Stamford Bridge.
However, the FA Cup defending champions are said to be targeting Sevilla's Andre Silva - who is on loan from AC Milan and could cost the Spanish League side £32 million to buy in the summer.
However, the interest in Vardy is rather curious given that he will turn 32 in just a few days and Chelsea are reluctant to sign players over the age of 30 - something that has created a stumbling block in any deal for Higuain.
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William has an official engagement in the day, meeting pilots and paramedics from London's Air Ambulance. Past year the heavily pregnant Duchess spent the day with her family at Kensington Palace .
However, this season Higuain hasn't been quite so productive in front of goal and he has struggled to win over the AC Milan fans.
The Argentinean global is now on loan at the San Siro from Juve but after starting life at Milan in superb form with 7 goals in his first 9 appearances, the striker is going through a dry spell having netted just once in his last 11 outings.
Sarri will hope to get the best out of Higuain, whose form in Naples saw him land a move to Juventus in a mouthwatering £77.9m move three years ago.
"Milan's sporting director Leonardo has had some very interesting things to say and he says it's up to Higuain now to make a decision". Seeing as he is here, he needs to knuckle down and actually do something for this team.
The former Real Madrid man opted against celebrating either of the goals he scored against Nottingham Forest at the weekend.