The Premier League champions then confirmed on Friday the Spain worldwide has signed a five-year deal, becoming their second arrival of the week after full-back Angelino was brought back from PSV.
"What City have achieved in the last two years has been incredible and I'm looking forward to being part of such a talented squad", he told City's website.
"I chose City because of the football challenge and the way these last two years they have won lots of things".
I don't look for the team, for the club.
Asked why City are considered a bigger attraction than rivals United, Rodri told reporters: "Maybe they have changed the story".
"For me it is a great step". Liverpool's era of dominance in the 1980s came to an end because too many players were allowed to grow old together.More news: Trump says 'unfair' defence treaty with Japan needs to be changed
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"So, for me, it's very important".
"Rodri has proven himself as a hugely talented, young midfielder", said director of football Txiki Begiristain.
"I think he has been the greatest defensive midfielder in last ten years for me, for Barca and Spanish national team", added Rodri.
Malian worldwide Kone and Mendes made 55 Ligue 1 appearances between them last season as Lille finished second, three points clear of third-placed Lyon.
Manchester City are reportedly ready to offer Fernandinho a new contract despite already signing his long-term replacement.
Rodri had three goals and one assist in 34 La Liga appearances for Los Colchoneros last season, while Herrera contributed with six goals in 33 Liga NOS outings for Os Dragoes. "He is flawless fit for Pep Guardiola's team and we are confident he will be a success", commented City's Director of Football, Txiki Begiristain.
However, the 34-year-old, now with the national team in Brazil for the Copa America final, struggled with injuries towards the end of last season.