The Argentinian forward is being shopped around by the Bernabeu club, but their valuation is £4m more than Gunners boss Arsene Wenger is reportedly prepared to pay.
The report claims Wenger has enquired about the 25-year-old already this season, and would be interested in bringing him to the Emirates Stadium.
Fiorentina striker Stevan Jovetic remains Arsenal's first choice, but the Gunners face competition from Serie 'A' champions Juventus for the Montenegrin.
Higuain reportedly earns around £120,000-a-week at Real Madrid, and Arsenal would have to break their wage structure to bring him to the club.
He's struggled to hold down a first-team place at the Bernabeu this term, with Karim Benzema often preferred to the Argentina international.
The report claims Higuain would be willing to move to the Premier League - and Manchester City were linked with a bid last summer.
But Arsenal's interest hinges on their ability to secure a top four finish in the Premier League this season. Their 4-1 home win over Wigan on Tuesday night means Champions League qualification is in their own hands heading into the final match of the season.
Arsenal face Newcastle at St James Park while Tottenham - their main competition for fourth spot - welcome Sunderland to White Hart Lane.