Manchester City value Rodri at more than €70 million (£60m / $81m) amid interest from Barcelona and Real Madrid, sources have told ESPN.
Barcelona have had an offer of €45m rejected for the midfielder. An agreement with Barcelona is still not close but there are ongoing talks, sources told ESPN.
Sources have told ESPN that City are aware of Rodri's desire to return to Spain, but will not sanction a cut-price deal.
Club bosses have not ruled out allowing Rodri to leave because they do not want to keep an unhappy player. Rodri's recent injury record, age and contract situation are also factors.
Barcelona had a bid rejected by Manchester City for Rodri. Carl Recine/Getty Images The 2024 Ballon d'Or winner has got one year left on his current deal and would potentially be a free agent next summer.
Sources have told ESPN that City will look to replace Rodri if he leaves. A deal for Lille's Ayyoub Bouaddi is considered separate because he is a long-term target.
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There are also doubts about the futures of Tijjani Reijnders, who is wanted by Nottingham Forest, and Nico González.
Meanwhile, City are closing in on the capture of Marseille goalkeeper Gerónimo Rulli. The Argentinian has been lined up to replace James Trafford, who has joined Leeds.
Information from ESPN's Sam Mardsen contributed to this report.