"Of course we want him to stay," Pogba told Sky Sports. "The results have been great. I have a great relationship with him, he has a great relationship with the players."
Solskjaer took the reins on a caretaker basis after Jose Mourinho was sacked in mid-December following an increasingly miserable tenure at Old Trafford. Since that time, United have cut their gap behind the top four from 11 points to just two and are in the Champions League quarterfinals.
Pogba's admiration of Solskjaer may also be linked to his apparently fractious relationship with Mourinho.
"When a player is happy, he wants to keep being happy," Pogba continued. "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."
Solskjaer's candidacy for the permanent gig is facing the most severe scrutiny since his Manchester United spell began. The team has suffered back-to-back defeats to Arsenal (Premier League) and Wolverhampton Wanderers (FA Cup), leaving the Champions League as the only conceivable chance of silverware this term.
Meanwhile, Pogba was pressed into talking about the finer details of Mourinho's sensational firing from the club, but he was typically guarded about the situation.
"Maybe we lost confidence, maybe things went wrong," Pogba said. "A lot of talking outside that we weren't used to. I don't like to talk about the past. I like to talk about the future because that's what matters.
"We are better now and the results have been brilliant. We are back in the (race for the) top four."
The Red Devils will take on Watford and Wolves before the first leg of their Champions League last-eight affair with Barcelona on April 10.