Roberts scored 15 goals in 43 appearances for Celtic during an 18-month loan spell that ended in May, and the Scottish champions were ready to spend £30 million to make him their player this season.
But City would only agree to a further season-long loan, leaving Rodgers frustrated.
"We would have broken our transfer record for Patrick," said Rodgers, speaking at a charity event in Belfast. "We wanted to find the deal that would get him back here. But he's a Manchester City player.
"We could have offered them £30m and they would have said no.
"They didn’t want to sell. So the best option was to get him back on loan."
Roberts, who has made just three appearances for City since joining the club from Fulham in 2015, expressed his relief that the Premier League club had kept the door open to him one day becoming a part of their team.
"Celtic did try to get the permanent move but, in fairness to City, they wanted to keep me and said that couldn't happen," Roberts told The Scotsman.
"It gives me a bit of hope obviously [City] still think I have a long-term future which is good for me. They will let me express myself up here and enjoy my season.
"The bigger picture for me is to be the best player I can be and play in the best league in the world. For me, it is just to improve every day and get better working with the manager here.
"You never know what can happen in football, so hopefully my career goes the way I plan it to be."