Pogba eventually left United after his contract ran down, but had a transfer request rejected by Woodward in 2019.
He told the Daily Mail: "I will tell you something I’ve never told anyone.
"The year Jose went and Ole came, it was my best season at United but after the last game I told Ole and Ed Woodward that I thought it was my last year and that I wanted to leave.
"I was 27 back then, it didn’t work out the way I wanted. I gave my best but I didn’t see the club going upwards.
"Manchester City and Liverpool were better than us and they were improving. Ole said yes (to me leaving) and that he would talk to Ed.
"My head was already that I wanted to go but I came back for pre-season because I wanted to be professional.
"I spoke to Ed to try to make a move but he blocked it. I didn’t want to play for United anymore but I had to be professional.
Mentally I wasn’t there and then I got the injuries."