Higuain, who's currently on loan at AC Milan, reportedly told the Rossoneri he wants to join Chelsea, but any deal would require the approval of parent club Juventus.
Johnson reports that Juventus would only sanction the switch if the Blues accepted Milan's loan terms, which includes a €36-million (£32-million) option to buy at the end of the season. A short-term or 18-month loan spell is out of the question, according to Johnson.
It's unclear if Chelsea director Marina Granovskaia will break the club's over-30 policy to sign the 31-year-old Higuain. Chelsea made an exception for Olivier Giroud in the last January window, but the Frenchman made little impact after arriving from Arsenal for a reported €12-million fee.
Milan manager Gennaro Gattuso suggested after Saturday's win over Sampdoria that Higuain had asked to leave.
"When a player makes up his mind, it becomes hard to convince them otherwise," Gattuso said.
Struggling Chelsea striker Alvaro Morata was considered a potential makeweight in a prospective deal with Milan, but it's believed the Spaniard prefers a move back to La Liga.
Chelsea manager Maurizio Sarri reportedly met with Higuain's brother in London to gauge his interest. Sarri helped the Argentine break the single-season Serie A scoring record while at Napoli during the 2015-16 campaign.