Following his dismissal by Reading after just six months in charge, Rodgers held talks with City administrator Brian Marwood to join the club as a first-team coach.
"I was grateful because it was good for my confidence at the time because I'd left Reading having had a long career in coaching and all of a sudden I was on the outside looking in," he is quoted as saying in The Telegraph.
"I went up at the end of the season, took a couple of days looking around the project and everything and I flew to Milan to meet Roberto out there.
"They were excited about what was happening there and I didn't really think I was going to get a manager's job so the next best thing was at least working with top players."
However, the chance to manage Swansea City was too much for Rodgers to resist.
"Then all of a sudden I got the opportunity to go to Swansea so to be the No 1. Irrespective of money and whatever contract, at a great club like Swansea was always going to be too good to turn down," he said.
"I hadn't had anything in writing from Man City but I probably would have [earned more money]."
Rodgers left Swansea in the summer to become the Liverpool manager.