Solskjaer’s arrival coincided with an uplift in form for Pogba, who scored four times in his first three games under his new boss.
The Manchester United midfielder has recently teamed up with world champions France ahead of their Euro 2020 qualifiers against Moldova and Iceland.
And Pogba was asked about the possibility of signing for Real Madrid, who have recently appointed fellow Frenchman Zinedine Zidane as their manager.
And Pogba didn’t exactly talk down the chance of signing for the Bernabeu club.
“Like I’ve always said, Real Madrid is a dream for anyone. It’s one of the biggest clubs in the world,” Pogba said.
His club future appeared in doubt during widespread reports of acrimony between him and Jose Mourinho, who was succeeded as manager by Solskjaer in December.
The 46-year-old signed a deal until the end of the season but Pogba says he has done enough to get the job full-time.
“Of course we want him to stay,” said Pogba, who is under contract until 2021.
“The results have been great. I have a great relationship with him; he has a great relationship with the players.
“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 we had before.”
When Mourinho was sacked, United were sixth in the Premier League, 11 points off fourth, but they are now fifth, three points behind third-placed Tottenham.