The 23-year-old became the most expensive British player in history when his £116 million move to Manchester City from Nottingham Forest was announced in June during the World Cup.
That deal was surpassed last month by the reported £117 million Chelsea paid Aston Villa for Morgan Rogers.
Anderson was introduced to City fans on Wednesday at the Etihad Stadium club store alongside latest signing Geronimo Rulli, plus Marc Guehi and Gianluigi Donnarumma.
"I was just golfing in Portugal and bumped into a few and had a nice chat and stuff like that, but I had a decision to make and I chose City," the England midfielder said when asked about his conversations with some United players on holiday.
Anderson, asked if United came close to persuading him to move to Old Trafford, replied: "No."
He started all of England's World Cup games except the third-place playoff win over France, including the semi-final loss to Argentina.
He is set to make his City debut in Sunday's Community Shield against Arsenal in Cardiff.
"No, I'm feeling comfortable," he said when asked if he was feeling weighed down by his huge price tag.
"I want to show everyone what I can do and try not to focus on it too much. But I'm sure over the season I can show people what I do best."