The Spain midfielder has been heavily linked with a move to the Premier League champions and has a reported €70 million (£62m/$79m) release clause in his Atleti contract.
Goal has reported that City have identified the midfielder as their priority midfield transfer target this summer.
City sporting director Txiki Begiristain has personally scouted the 22-year-old this past season and has come away impressed with his abilities.
City are keen on bolstering their options at defensive midfield with Fernandinho now 34 and Rodri has done little to quell speculation he could fill that particular transfer wish of Pep Guardiola.
Speaking to Deportes Cuatro, the 22-year-old said: "I asked the club for peace of mind to give me space.
"It would be hypocritical to say that I can guarantee anything.
"The only thing I can say is that I have a contract with Atletico Madrid, I have a clause, I have some conditions and today I am happy here.
"I cannot say anything else because I do not know what's going to happen."
However, Goal understands that City's interest in Ndombele has cooled, while a move for Rice has been ruled out with the England midfielder also linked to Manchester United.
That has made a move for Rodri a priority for City this summer, with Ilkay Gundogan's future with the club also up in the air.
The German midfielder has not made progress on a contract extension, though he now says he is ready to re-open talks with the club over a new deal.
Guardiola also deployed John Stones at central midfield as times during the 2018-19 season, with the 25-year-old falling back on the centre-back depth chart.
Fabian Delph is also an option for City in the middle of the park, but the 29-year-old could move on in the summer with playing time hard to come by in 2018-19.