Arsenal officials will have to wait for final approval from Arsene Wenger to sign Rodrigo from Benfica, according to Portuguese newspaper O Jogo.
The Gunners have been searching far and wide for reinforcements up front after Theo Walcott suffered a season-ending knee injury against Tottenham in the FA Cup.
Rodrigo, 22, has drastically improved at the Estádio da Luz this season and has drawn interest from Arsene Wenger as a result.
Arsenal had been tracking the Brazilian-born striker for a while, but looked set to miss out after Zenit St. Petersburg reportedly agreed a €30m fee with Benfica. However, Rodrigo had no intention of moving to Russia and only has eyes for one of Europe's major leagues.
Buoyed by the news, Arsenal officials made contact with the Portuguese outfit and are confident of agreeing a deal, with a figure of less than €30m thought to be enough.
Once Arsenal officials agree a deal, they'll report back to Wenger, who will give the green light on a transfer deal.
It is thought that Wenger will make a decision depending on the price and whether he believes he can sign other targets for less.
If the frugal Frenchman believes he can find better value elsewhere, a potential deal will be put on ice until the summer at least.