The France international has been regularly linked with a move to Spanish giants Real Madrid in the summer transfer window.
Real Madrid boss Zinedine Zidane is thought to be a big admirer of the World Cup winner as the France legend looks to bolster the los Blancos team.
The 26-year-old’s future will remain a source of debate until the European transfer window closes in Italy and Spain next month.
However, Solskjaer was keen to emphasise that he isn’t worried about Pogba’s future at the 20-time English champions.
“I’ve got no concerns on Paul. For me, he is going to stay,” Solskjaer told Sky Sports.
“I don’t think it is odd saying, ‘I enjoy playing, I have fun with my team-mates, I enjoy what I’m doing, I love my job – and I’ve enjoyed the game’.
“Of course, that sentence with the question mark about him – there’s always question marks about Paul Pogba.
“There’s not one press conference where I have not answered a question about Paul Pogba.
“Eighty per cent of what he said is ‘I enjoyed the game’ and his time now.”
Manchester United were 4-0 winners over Chelsea FC in their Premier League opener at Old Trafford earlier this month.
Pogba created two assists to help Solskjaer’s side made a perfect start to the Premier League season.
Manchester United have only finished in the Premier League’s top four once since Pogba’s move to Old Trafford in 2016.
The Red Devils signed Pogba in a club record £89m deal from Serie A giants Juventus despite having sold the midfielder to the Italian club in 2012.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news