The Brazilian has most frequently been linked with Arsenal, though the winger has never appeared close to actually leaving Real Madrid.
"I'm used to it. Every year I'm reported to be leaving. During the transfer window I was linked with a new club nearly every week," Rodrygo said this spring.
New information has now emerged about the 25-year-old's future.
According to Spanish outlet Mundo Deportivo, Real Madrid are open to selling Rodrygo during the summer transfer window.
The forward made just 10 starts for the club last season, having been hampered by a serious knee injury.
Rodrygo suffered a torn ACL and meniscus in his right knee in a March defeat to Getafe, requiring surgery and ruling him out for the remainder of the season.
The injury also cost him a place in Brazil's World Cup squad, with the timeline for a full recovery only allowing him to return in time for pre-season with his club.
According to the new reports he remains focused on returning to action under his current contract rather than forcing through a move this summer.
Rodrygo wants to reclaim his place in the first team, but Mundo Deportivo report that head coach Jose Mourinho will not stand in the way should clubs come calling. Arsenal have been raised as a potential desintation.
The forward is said to be one of several Real Madrid players considered available as Mourinho looks to reshape his squad following a season without a major trophy, with Eduardo Camavinga another name reportedly open to a transfer.
Rodrygo joined Real Madrid from Santos in a €45m move in 2019 and has gone on to help the club win two La Liga and Champions League doubles, establishing himself as a regular alongside Vinicius Junior and Kylian Mbappe in attack before this season's injury problems took hold.
It remains to be seen whether Arsenal or any other club will turn its interest in the forward into something concrete this summer.
Rodrygo is contracted to Real Madrid until the summer of 2028.