The 37-year-old returned to Old Trafford last year and enjoyed a successful 2021-22 campaign on a personal level, finding the back of the net on 24 occasions in 37 appearances, in addition to registering three assists.
Man United ended the season without a trophy, though, and finished down in sixth spot in the Premier League table, meaning that they will not play in the Champions League next term.
According to The Times, Ronaldo has asked to be allowed to leave the 20-time English champions this summer should they receive a suitable offer for his services.
The report claims that a desire to play in the Champions League next term is driving the attacker's decision, as he wants to be competing for the biggest trophies in the latter stages of his career.
Ronaldo allegedly does not believe that his current side are in a position to challenge for major trophies, while they are yet to make a single signing during this summer's transfer window.
According to Sky Sports News, the forward is 'in love' with Man United and has huge respect for the club, but he wants to leave for personal reasons, as he is desperate to win at least one more European Cup.
The Red Devils are said to be determined to keep hold of Ronaldo, with the Portuguese still having one year left to run on his contract at Old Trafford, and the option of an additional 12 months.
An exit for the former Sporting youngster would leave Man United desperately short of centre-forward options, meanwhile, as Edinson Cavani has left the club on a free transfer this summer.
Ronaldo is due back at the club's Carrington training complex on Monday for pre-season training, with the team due to fly out to Thailand on July 8 ahead of their first friendly of the summer against Liverpool four days later.
The attacker's frustration at his team's summer business could be eased in the near future, as deals for Barcelona's Frenkie de Jong, Feyenoord's Tyrell Malacia and free agent Christian Eriksen are advanced.
Speaking at his first press conference as Man United boss, Ten Hag said that he was looking forward to working with Ronaldo next season.
"Of course (looking forward to managing Ronaldo). Ronaldo? Goals! (what will he bring). I talk first with Ronaldo before I talk with you," said the new Red Devils manager.