He claimed in an interview that the transfer was "close" but City sources have insisted his comments are "not reflective" of their interest at the time, which has been described as "mild."
Ronaldo, 37, claims only Sir Alex Ferguson's intervention stopped him from joining City, despite his highly successful first spell at rivals United between 2003 and 2009.
"I think it was the key, it was the difference in that moment, but I cannot be loyal if I will, I wouldn't say that Manchester City wasn't close," Ronaldo said.
"I spoke with [Ferguson]. He said to me that, 'It's impossible for you to come to Manchester City,' and I say, 'OK, boss.'
"Well, honestly, it [joining City] was close... It's something they spoke [about] a lot and [City manager Pep] Guardiola said two weeks ago, I guess, that they tried hard to have me."
The second part of Ronaldo's interview is set to air Thursday with sources telling ESPN that United will wait to discover the full extent of his comments before making a decision on his future.
United, according to sources, are already furious about parts of the interview, particularly Ronaldo's claim that there has been "zero progress" at the club since Ferguson retired in 2013 and his revelation that he "doesn't respect" manager Erik ten Hag.
United have rejected Ronaldo's claim that their Carrington training ground has not been updated since he left for Real Madrid in 2009 and insist money has been invested to renovate the restaurant, swimming pool and gym in the past 12 months.
Sources have told ESPN that Ten Hag does not believe he can work with Ronaldo again while the majority of players do not think there is a way back for the forward at Old Trafford after the World Cup.
United, according to sources, are taking legal advice about how best to deal with the situation.