"We want him to stay. The results have been great. I have a great relationship with him, he has a great relationship with the players," Pogba told Sky Sports.
"When a player is happy, he wants to keep being happy. Solskjaer deserves it. He knows the club, he knows everything about the club. He is a really happy coach that gave confidence back to the players.
"This gave us the freedom to play and enjoy football again because maybe we lost that with the results that we had before."
Despite winning the World Cup with France last year, Pogba struggled for form under Mourinho who benched him, but the 26-year-old is back to his best under Solskjaer with nine goals and seven assists in all competitions.
"Maybe we lost confidence, maybe things went wrong. A lot of talking outside that we weren't used to," Pogba said, reflecting on the final part of Mourinho's tenure.
"I don't like to talk about the past. I like to talk about the future because that's what matters. We're better now and the results have been brilliant."
United are fifth in the Premier League with 58 points from 30 matches and within three points of third-placed Tottenham Hotspur. They take on Barcelona in the last-eight of the Champions League next month.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
