The Spain international has emerged as a top target for the Premier League champions and his current club admit that he could be lured elsewhere
Manchester City have seen the transfer door left open to Atletico Madrid midfielder Rodri, with the Liga club aware that tempting offers may be tabled this summer.
Enrique Cerezo, club president at Wanda Metropolitano, is running the risk of losing several senior stars at the end of the 2018-19 campaign.
Long-serving defender Diego Godin has confirmed that he will be departing once his current contract expires.
Antoine Griezmann, meanwhile, has informed Atletico of his desire to leave amid ongoing links to Spanish champions Barcelona.
It could be that Rodri follows them through the exits, with Goal having revealed Cityâ€™s interest in the 22-year-old.
The Premier League title holders are aware of a â‚¬70 million release clause in the Spain internationalâ€™s contract and are considering triggering it as they seek a long-term successor to Fernandinho.
Cerezo acknowledges that interest may be shown and that there is little he can do about it.
He told El Partidazo when quizzed on the Rodri rumours: "Today... today,Â RodrigoÂ is anÂ AtleticoÂ player.
"But if tomorrow he has an offer and wants to go..."
Atletico are reluctant to see a number of star names slip their net, but are resigned to the possibility of that happening.
Griezmannâ€™s stance has frustrated many in the Spanish capital, with the World Cup-winning France international having committed to a new contract last summer after bringing an end to one long-running transfer saga.
"[Diego] SimeoneÂ is disappointed, like the others,"Â CerezoÂ said of the France international.
"He was determined to leave and there was no chance of convincing him.
"I don't know or care [whoÂ Griezmann's next team will be]. But when a team wants to pay a release clause, it's normal to communicate [your intention to do so] and we haven't received any messages from anyone just yet.
"Wherever he goes, I hope that he is treated the same as he was here... and good luck!"
Griezmann has a â‚¬120m release clause in his contract that those at Camp Nou â€“ having missed out on a top target in 2018 â€“ are said to be mulling over.