Manchester United have been linked with Tchouameni throughout the summer despite having already added Andrey Santos from Chelsea and Youri Tielemans from Aston Villa to their midfield options, with the club still seeking a more defensive-minded signing to complete the rebuild under Michael Carrick following the return of Champions League football.
According to The Sun, Real Madrid are now prepared to sanction Tchouameni's departure in order to help fund a move for Rodri, valued at around £85m, with the Spain international coming off Spain's World Cup triumph but having just a year remaining on his City contract.
Real Madrid's growing need for funds has been sharpened by their pursuit of RB Leipzig winger Yan Diomande, which is expected to require a significant outlay of its own. Tchouameni, valued at around £68m and previously involved in a heated on-field confrontation with Federico Valverde last season, only recently signed fresh terms at the Bernabeu, but France's disappointing World Cup exit has left him assessing his options regardless.
Jose Mourinho is reportedly reluctant to lose the 26-year-old but would be prepared to do so if it clears the path to signing Rodri, according to the Mirror.
United's midfield rebuild has been a key focus of the summer following their return to the Champions League, with the club having identified the position as needing further reinforcement even after the arrivals of Santos and Tielemans.
Should Real Madrid's pursuit of Rodri progress as expected, Tchouameni's situation is likely to become clearer in the coming weeks, with United positioned as one of the leading candidates to take advantage of any resulting sale.
Mancheser City, for their part, are hopeful Rodri can be persuaded to sign a new contract at the Etihad, though the midfielder is understood to have already agreed personal terms with Real Madrid, leaving the outcome largely dependent on the two clubs settling on a transfer fee.