Higuain is Maurizio Sarri's number one choice to replace Alvaro Morata, who is expected to leave Stamford Bridge this month.
And the Stamford Bridge outfit have now began complicated negotiations with Juventus and AC Milan over the Argentine worldwide.
Higuain is keen to join Chelsea as well and his brother was in London this week to negotiate potential figures.
According to British news media outlet The Sun, Higuain is Chelsea's main target in the winter transfer window. Their only option is to take over the existing deal to sign him for the remainder of the season which would require them to pay a loan fee on top.
The Argentina global is on loan at San Siro from Juventus this season but has been heavily linked with a move to Stamford Bridge in this month's transfer window.
Milan boss Gennaro Gattuso revealed on Saturday that the Argentina worldwide wants to leave San Siro before the end of the month, and Chelsea boss Maurizio Sarri is keen on a reunion, three years after last working with the striker at Napoli.
Speaking after his Milan side overcame Sampdoria in the Coppa Italia round of 16 to secure a hard-fought 2-0 win in extra time, Gattuso admitted he doesn't know what will happen with Huguain but claimed it is hard to change a player's mind once they have made a decision. 'There is great honesty. When a player makes certain choices, it becomes hard to convince him otherwise.
At the moment, he's our player and we're holding on tightly to him.
"We are honest with each other and I want him to maintain this attitude, which has never been lacking thus far", Gattuso told Milan TV after the game.
Higuain was however shipped out to AC Milan in the summer following the £100m arrival of Cristiano Ronaldo, initially on a season-long loan, with the Rossoneri having already agreed a deal to make it a permanent move next summer, a deal which totals around €54m.