Under, who has four goals in eight caps for Turkey, was heavily courted by European sides as he engineered a move away from Super Lig club Basaksehir after just one season.
The 20-year-old winger was initially eased into Roma's first team but has since taken up an important role in Eusebio Di Francesco's starting XI to score six goals in 24 appearances.
Although his side sit third in the Serie A table this term, Under has no regret over his choice to snub one of Europe's most powerful teams.
"I received an offer from Manchester City, but I did not agree," he told Spor Arena. "There was the project in Rome, and the attitude of the club and the coach was important to me.
"Then, with the sale of Salah, the team has become more suited to my characteristics."
Under was brought to the capital club by renowned technical director Monchi, who expects him to become a vital part of the team in the coming years, while he is enjoying life under Di Francesco too.
"Monchi is a very important name and has always had a lot of confidence in me and I feel it. He says I can become an important player for the future of Rome, important in discipline and tactical work.
"Di Francesco gives all players a chance, trusts them and keeps on encouraging them. He always wants the best in training and we have a good relationship ".
"The biggest problem was the language, now things are better and I'm more sociable.
"One day I got out of the shower after training and Monchi told me that I had to meet someone. I went and it turned out to be Francesco Totti! I was very excited, but I feel unlucky not to have played with him."
The young winger may have missed the chance to play with one legendary figure, but there are many more well known figures still going that he looks up to, as he gave a full 11 of his favourites.
"Lionel Messi is the best in the world, and I really like David Silva too. My ideal 11 would be Alisson in goal, defended by Dani Alves, Sergio Ramos, Thiago Silva and Marcelo, then Luka Modric, David Silva, Kevin De Bruyne, Salah, Messi and Cristiano Ronaldo."