Real Madrid are still trying to sign the World Cup winner before the European transfer window shuts on September 2.
"You always put question marks around Paul, don't you?" Solskjaer asked the journalists gathered for his weekly news conference.
"I've got no concerns on Paul. For me, he is going to stay," the United boss continued.
"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."