The Serie A side are said to want £40m for the striker but it remains to be seen if Chelsea would be prepared to meet their valuation.
The Premier League champions are desperate to overhaul their squad after a disastrous season which sees them languishing in 13th place in the table.
With the futures of Costa, Loic Remy, Radamel Falcao and new recruit Alexandre Pato uncertain, the Blues have made a swoop for Higuain a top target.