Higuain has netted eight times in 20 matches for Milan.
Spanish newspaper Marca is reporting that Higuain could be set for a reunion with Maurizio Sarri, who has previously worked with the Argentina striker at Napoli.
One stumbling block is that Milan want a replacement for Higuain before allowing the Argentine to leave but Chelsea are believed to be willing to offer Morata as a makeweight in the deal.
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He scored 91 goals during his three years at the club before moving to Juventus in 2016 on a 90 million euro deal.
However, Milan sporting director Leonardo warned on Tuesday he had to get down to work.
When asked about Chelsea's interest in Higuain, Leonardo said: "There's no point following rumours and gossip".
We'll have to wait and see how things develop but as much as Higuain would be an exciting addition for Chelsea, it would also be something of a risk to sign a 31-year-old who's never played in the Premier League and may take some time to adjust to life in England.
"We want to continue to take the club forward and the team forward, and to do that, we've got to keep our best player".