The news was first reported by The Times.
The Portugal captain returned to United a year ago for a second stint at Old Trafford and scored 18 goals in 30 league appearances, but the team finished sixth in the Premier League and did not qualify for next season's elite European club competition.
Ronaldo, 37, has a contract with the Red Devils until June 2023, with an option to extend it for a further year, but has now asked to be transferred.
Sources have told ESPN that United have informed Ronaldo that he is not available for transfer this summer and that they expect him to stay for the remaining year of his contract.
Despite his stated respect and love for United and their fans, the former Real Madrid star feels he needs the motivation of playing in the Champions League in the last stage of his career. Ronaldo is said to view playing in the Champions League and competing for major trophies as essential.
United has appointed Ajax head coach Erik ten Hag to replace interim coach Ralf Rangnick, and during his unveiling last month, he said that Ronaldo was part of his plans for the coming season.
Ronaldo first joined United from Portuguese side Sporting CP in 2003.
He scored 118 goals in 292 games before leaving for Real Madrid in 2009, where he remained until joining Juventus in 2018.
Ronaldo failed to win the Champions League with Juve in his three seasons with the Turin giants, but he lifted the trophy with United in 2008 and four times with Madrid. He was the top scorer in Serie A for the last two seasons he was in Turin and scored 101 goals in 134 appearances.
The former Real Madrid star has won 32 titles in his career, including seven league titles and five Champions Leagues.
He captained Portugal to Euro 2016 glory and the 2019 UEFA Nations League.
A five-time Ballon d'Or winner, Ronaldo is the men's world-record holder for most goals scored (117) in internationals.
He is set to captain Portugal at the World Cup later this year.
Information from ESPN FC correspondent Rob Dawson was used in this report.