According to TalkSPORT, Arsenal are prioritising the signing of a new winger this summer and the 24-year-old is high on their shortlist.
The report adds that Rodrygo is frustrated with his role at Real Madrid as he is playing 'second fiddle' to superstars Kylian Mbappe and Vinicius Junior.
It’s understood that Real Madrid would be interested in cashing in on the Brazilian, who they value at £85 million, in order to raise funds for a defensive overhaul.
ESPN’s Sam Marsden said there is 'more than a suggestion' the winger could leave Madrid this summer.
"I think that Real Madrid have to make a big decision this summer. Rodrygo seems to be the one that's being pushed towards the door, I think one of Rodrygo or potentially even Vinicius Jr has to go," he told talkSPORT.
"Rodrygo has made it clear he wants to play on the left, he's been playing on the right at Real Madrid so he's the most obvious one to go.
“But Vinicius Jr might be a bigger money-spinner and may actually fix their problems a little bit more because they've kind of got that status problem between Vinicius Jr, Mbappe, (Jude) Bellingham in the shadows as well. Maybe Xabi Alonso can make it work, but it's not worked at all this season."