"We spoke about it. He said it to me at first. I was just going to leave it, but he had a joke about it. There are no hard feelings," the former Southampton full back told British media.
"I just thought that I had a better chance of playing at United (than at Chelsea). Patrice Evra was leaving (United), whereas Chelsea had a solid back four that I knew Jose liked.
"So even though Chelsea were much closer to my home, I felt United were the better choice. I was never focused on the money. It was about football."
Shaw, who suffered a double leg fracture last year, has started the season strongly, with his performances meriting a call up to manager Sam Allardyce's England squad for Sunday's World Cup qualifier against Slovakia.
Shaw also said he was relishing the battle with Tottenham Hotspur defender Danny Rose for the England starting role.
"I watched a lot of football while I was out and I always look to see what other left backs are doing and how they play, how I can improve my own game," he said.
"There have been a lot of good English left backs who have emerged over the past year, especially Danny Rose, who was the best in the league last season. I want to be playing with the best and fighting for a position against the best players."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
