The 27-year-old midfielder is unsettled at the Bernabeu after a disappointing first season in the Spanish capital.
Manchester United have been long-term admirers of Modric, but the report claims Arsenal have now turned to the Real Madrid playmaker after failing in their pursuit of their top targets so far.
The Gunners lost out in the race for Gonzalo Higuain - he's joined Napoli - and they've had several bids knocked back by Liverpool for striker Luis Suarez.
Even Brazil international Bernard looks set to join Porto or Shakhtar Donetsk rather than Arsenal.
United's desire for a central midfielder is more pressing though, and they've missed out on targets of their own.
Thiago Alcantara was at one stage seemingly set to become a Manchester United player this summer, but Bayern Munich swooped in at the last moment. The lure of Pep Guardiola proved too much, and Thiago plumped for the European champions.
Cesc Fabregas, Thiago's former-Barcelona teammate, then became top priority, but the Spanish giants have so far refused to entertain offers for the 26-year-old midfielder.
And the report claims both Arsenal and Manchester United have now turned to Modric - a player who could be expendable at the Bernabeu following the double capture of Isco and Asier Illarramendi.