The midfielder had already revealed that he will retire in May but stay on at Old Trafford in a coaching role, revealing to the English newspaper that he hardly had to think about the decision.
Carrick said: "I didn't even have to think about it. It was a total no-brainer. Working with Jose [Mourinho]. I'm genuinely looking around and thinking "not many lads would get that opportunity so quick".
"It's an unbelievable opportunity to learn off somebody like Jose who has been everywhere and won everywhere. He's got something very special. He's a winner. He's got that drive to succeed."
The 36-year-old also reflected on his illustrious career at United, in which 18 trophies including five Premier League titles and one Champions League.
"I had the best times under Sir Alex Ferguson. We had five leagues and three Champions League finals in seven years.
He concluded: "We had a great squad, a great time. Winning the Champions League in Moscow (in 2008), without doubt, was the best feeling I have ever had."