Blues boss Maurizio Sarri is a huge admirer of the Argentina striker, who is currently on loan at AC Milan from Juventus.
Milan paid Juve a £16million loan fee at the start of the season and can make the deal permanent in the summer by paying an extra £32m.
It had previously been reported that they were keen to cut the loan short which would allow him to move to Chelsea in the January transfer window.
That means Chelsea will have to delay their swoop, although, the reports also claims Juventus will be happy to sell in the summer if they can match the £32m asking price.
Sarri is desperate for a proven goalscorer to challenge misfiring duo Alvaro Morata and Olivier Giroud, and knows Higuain well having overseen his most prolific season when the pair worked together at Napoli.
In the 2015/16 campaign, Higuain scored 36 goals in 35 Serie A matches and earned a move to Juventus as result.
Sarri has made no secret of his admiration for the player and revealed he would love to work with him again.
“I miss Higuain a great deal,” he said in October.
“I miss him because he’ll keep scoring goals until the day he dies. ‘He is a goal machine, a systematic and automatic jackpot.”
Since moving to Milan he has struggled in front of goal, with just one strike in his last 10 appearances in all competitions.
That prompted speculation the club would look to offload him but he now looks set to stay and Milan sporting director Leonardo has urged him to turn his fortunes around.
“He has to make a decision and take on his share of the responsibility,” the Brazilian said.
“Not this continual, ‘yes, no, I’m not sure.’
“He had a tough moment, he has to put it behind him and get to work.
“There’s no point following rumours and gossip. He is here right now.
“Seeing as he is here, he needs to get down and actually do something for this team.
“A goal can change things, but if he is to continue here, he needs to take on responsibility.”