The 45-year-old says he was "in awe" of United manager Jose Mourinho when the Portuguese took charge of Chelsea, while he was Fulham's Under-18 coach.
The duo later worked together when Clement - who was appointed Swansea manager in January - took a job at Chelsea's academy.
"It was brilliant for me," he said.
"He was the professor and I was the student."
Swansea travel to Old Trafford (12:00 BST) three points adrift of safety with four games remaining.
Clement said he had learned a lot from Mourinho, who he said kept players and staff on their toes.
He added: "You were never quite sure where you stood with him.
"He created a distance between people. He was very strong on the psychological side, on managing people - both players and staff."
Paul Clement faces a man he once regarded as "the professor" when he takes his Swansea City side to face Manchester United on Sunday.