Arsenal have been heavily linked with a summer move for the Brazilian, whose playing time has been limited recently due to injury and illness.
Reports from Germany suggest that the Gunners are actively searching for a new winger, with Rodrygo among their potential targets.
While discussions over a transfer have reportedly taken place, his substantial wage demands could pose a challenge in finalizing a deal.
The likelihood of a move may increase with the changes happening at Real Madrid this summer. Ancelotti is set to leave his role to take charge of the Brazil national team, with Xabi Alonso stepping in as his replacement.
Madrid wrapped up their season with a victory over Real Sociedad, marking a farewell for several key figures.
Alongside Ancelotti, club legend Luka Modric and midfielder Lucas Vazquez—affectionately known as Cafucas by his teammates—will also be departing.
Rodrygo, who previously shared a farewell message for Modric, has now extended his gratitude to both Ancelotti and Vazquez.
On Instagram, he shared pictures of himself with Ancelotti with a message reading: “Mister, I can’t begin any other way than thanking you for EVERYTHING!
“You’ve written one of the most incredible chapters in Club history: the coach with the most titles. And I was lucky enough that our paths crossed, a dream come true.
“I take all the conversations, advices and scolds but most importantly, your affection and those unforgettable hugs in both victory and defeat.
“You’re not just a coach. You are a mentor and a friend. Together we win Spain, Europe… and the world. Now we’re going to conquer the world once again, this time with the yellow shirt.
“Let’s keep writing our story together. I love you, Mister!”
He also shared a picture of him and Vazquez on his story, with a message reading: “Cafucas my brother. Thank you for these years and especially for the friendship. You deserve the best!”
He then shared a squad picture of the team in front of big screens at Santiago Bernabau that read: “Gracias Carlo” and “Gracias Luka.”