The 37-year-old told the TalkTV host he felt betrayed at the club and that manager Erik ten Hag and the United hierarchy are trying to force him out.
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Now the Premier League giants have made a statement on their website.
It reads: "Manchester United notes the media coverage regarding an interview by Cristiano Ronaldo.
"The club will consider its response after the full facts have been established.
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"Our focus remains on preparing for the second half of the season and continuing the momentum, belief and togetherness being built among the players, manager, staff, and fans."
The full 90-minute interview was conducted at the request of the five-time Ballon d'Or winner, Piers Morgan revealed to talkSPORT on Monday.
It will be broadcast on the Piers Morgan Uncensored Show on TalkTV across Wednesday and Thursday evening.
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Excerpts have been unveiled ahead of the full interview being played out, in which Ronaldo gave explosive responses to his situation at United.
When asked if United's hierarchy were trying to force him out of the club, Ronaldo said: "Yes, not only the coach, but another two or three guys around the club. I felt betrayed."
When quizzed again if senior club executives were trying to oust him, Ronaldo replied: "I don't care. People should listen to the truth.
"Yes, I felt betrayed and I felt like some people don't want me here, not only this year, but last year too."
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Ronaldo wanted to leave United in the summer, but did not get his desired move away.
His relationship has only deteriorated as the season has progressed and he refused to come on as a substitute against Tottenham in October.
In the interview with Morgan, Ronaldo - who rejoined United in 2021 - also said he did not respect boss Ten Hag and accused the club of failing to show any progress from his first spell at Old Trafford.
He said of Ten Hag: "I don't have respect for him because he doesn't show respect for me. If you don't have respect for me, I'm never gonna have respect for you."
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On the club's lack of success since 2013, he said: "I don't know what is going on, but since Sir Alex Ferguson left I saw no evolution in the club, the progress was zero.
"For example, we have an interesting point that how the club as Manchester United, after (they) sack Ole (Gunnar Solskjaer), they buy - they bring (in), sports director Ralf Rangnick, which is something that nobody understands.
"This guy is not even a coach. A bigger club like Manchester United brings (a) sports director - surprised not only me but all the world, you know.
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"Nothing changed. Surprisingly. Not only the pool, the jacuzzi, even the gym…Even some points, the technology, the kitchen, the chefs, which is, I appreciate, lovely persons.
"They stopped in a time, which surprised me a lot. I thought I will see different things…different, as I mentioned before, technology, infrastructure.
"But, unfortunately, we see many things that I used to see when I was 20, 21, 23. So, it surprised me a lot."
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More on Cristiano Ronaldo:
Cristiano Ronaldo tells Piers Morgan he feels 'betrayed' by Manchester United, has no respect for Erik ten Hag and blasts state of club in explosive interview
Piers Morgan reveals Cristiano Ronaldo ASKED HIM to do interview which has stunned Manchester United and explains motives behind stinging attack on club and Erik ten Hag
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