Current Chelsea forward Didier Drogba is expected to leave Stamford Bridge at the end of this season and Gonzalo Higuain is rumoured to be a possible £35m replacement for the Ivorian.
A Chelsea source told The Sun: "Higuain is top of the shopping list.
"He has a phenomenal goalscoring record for Real and for Argentina but he helps make lots of goals too.
"He would be perfect for us, the sort of player who would thrive in the Premier League."
Higuain has scored 25 goals for Real Madrid this season.