Sources told ESPN that City boss Pep Guardiola and Ronaldo spoke on the phone on Thursday morning ahead of his possible departure from Juventus.
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Obstacles would still have to be overcome before the transfer is done -- particularly Juventus' demand for a fee -- but there is cautious optimism a deal can be reached, sources said.
Juventus would want around €28 million before allowing Ronaldo to leave but there is a keenness to get the 36-year-old off the wage bill.
Ronaldo and his team have communicated to Juve officials that he wants to leave the club now and won't be part of the squad for next Saturday's game against Empoli.
ESPN reported in June that Ronaldo's representatives were gauging interest from Europe's top clubs amid the possibility he could move this summer.
City initially were approached by Ronaldo's camp and while they were originally cool on the idea, their interest increased following confirmation on Wednesday that Harry Kane will stay at Tottenham Hotspur in this window.
Juventus coach Massimiliano Allegri is said to be "relaxed" about the possibility of losing Ronaldo, according to ESPN sources, but would want the club to sign another forward if he goes. The summer window is set to close on Aug. 31.
Sources have told ESPN that City and Juventus are yet to open talks about a deal and it is likely a compromise would have to be reached over the asking fee.
Ronaldo, who recently hit out on Instagram over "disrespectful" transfer talk, featured as a second-half substitute as Juventus began their season with a 2-2 draw with Udinese on Sunday. He withdrew from training on Wednesday with an apparent arm injury.
He has scored 101 goals in 134 appearances for Juventus since arriving from Real Madrid in 2018.
Information from ESPN correspondent Rob Dawson was used in this report.