The Daily Mail reports that the Gunners sees Rodrigo as a potential replacement for Robin van Persie.
Van Persie’s contract with Arsenal is set to expire at the end of next season and the striker has recently been linked with the likes of Manchester City, Real Madrid and Barcelona.
But Arsenal face a battle with Inter Milan for the highly-rated Spain Under 21 striker.
Rodrigo has an £18million release clause in his contract with Benfica.