Real Madrid have been strongly with a move for the World Cup winner in the summer.
Reports on Thursday also suggested he is ‘tearing apart’ the Manchester United dressing room and his agent cancelled a meeting to discuss a new contract.
But at Solskjaer’s press conference ahead of Sunday’s clash with Chelsea, he said: “You can’t guarantee anything in football but yes, I think Paul is going to be here.
“I can assure you he is very determined to succeed at Manchester United.”
Pogba was a surprise inclusion in the PFA Team of the Year and was the only non-Liverpool and Manchester City player to be selected.
Solskjaer also defended his selection despite his erratic form during the season.