The Argentina striker also confirmed that Chelsea and Liverpool had made inquiries about securing his services. Instead Tevez opted for a move to Manchester City after his extended loan deal at United ended, signing a lucrative five-year deal at Eastlands.
"Real made an offer but there was no agreement," Tevez told the Nation newspaper during a promotional visit to Abu Dhabi with his new club.
He added: "There were talks about deals and agreements but in the end it was only City. They showed lots of interest in me and are intent on growing and signing big players.
"I am sad to leave United but I am excited to join City. I'm thinking about the future and I will grow with this club."
Meanwhile manager Mark Hughes is continuing his pursuit of Emmanuel Adebayor and John Terry. Hughes remains determined to land the two men even though there are suggestions that Adebayor is not keen to leave Arsenal for Eastlands while Chelsea are adamant Terry is not for sale. Adebayor knows as well that there is stiff competition for places in attack at City following the arrivals of Tevez and Roque Santa Cruz with Craig Bellamy also on board.
Terry is Chelsea's defensive rock but Hughes believes the England international is ready for a new challenge.
"We do need new players," Hughes told the Gulf News. "We are still in discussions (over Adebayor) and the talks will continue.
"We have got attacking-minded players but we are looking to bring other players to the club before the transfer window closes.
"We are also looking to strengthen the defence. Every transfer deal is difficult and has different problems. There are areas which we need to address but we are happy with our progress."