Arsenal manager Arsene Wenger has reportedly identified Rodrigo as the ideal player to bolster his attacking options at the Emirates Stadium.
Wenger is believed to be keen to ease the burden on Olivier Giroud, who is the only senior frontman in the Arsenal squad, with Nicklas Bendtner out injured.
The Gunners had been linked with Juventus's Mirko Vucinic, but Wenger has now turned his attention to Benfica centre-forward Rodrigo, according to O Jogo.
The report went on to add that Wenger would look to sign the Spaniard on loan until the end of the season with a view to a permanent transfer.
Back in 2010 Rodrigo had a spell with Bolton Wanderers.