The Sun claims to be in contact with a "top Chelsea source" who revealed that the Argentinean has been identified as the man to replace veteran Blues star Didier Drogba.
"Higuain is top of the shopping list," the source told the Sun.
"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."
The newspaper reports that crucial to the deal will be whether or not Madrid boss Jose Mourinho is successful in his bid to lure Manchester City's Sergio Aguero to the Bernabeu next season.
Higuain is contracted to Madrid until 2016 and in January, the player's agent, who is also his father, insisted that the striker has no intention of leaving.
Higuain has scored over a 100 goals for the club since signing from River Plate in 2006.