The France international left Juventus for United in a world-record deal worth almost £90million in August 2016, returning to the club he departed in 2012, but he could just as easily have continued his career in La Liga had he wanted to do so.
"I came to Manchester United because I have certain goals. It is a big challenge for me," Pogba told SFR Sport.
"I could also have joined Real Madrid or Barcelona, who were interested in signing me. But I chose to return to United because I followed my heart.
"I want to win trophies with Manchester United, I never won anything here. I always told myself that I would one day return to United. It is a club I love a lot and I had unfinished business here. I left because I wanted to play more, but I felt that I was not done here yet.
"I am not even thinking about the transfer fee. I came here to play football."
Pogba has developed into a key figure at United after a difficult start to his second spell at Old Trafford, but he struggled in the 1-1 draw with Liverpool and conceded the penalty that led to James Milner's opener by handling in the area.