Solskjaer will leaning heavily on the quartet to lead Manchester United to a top-four finish as well as winning the FA Cup and Europe League.
Asked who United's leaders are, Solskjaer told the High Performance podcast: "You have had an example lately in Marcus Rashford - what kind of human being he is, but also a leader. He stepped forward on and off the pitch. He took his first penalty for Man Utd ever, added time, PSG, Champions League and he scored it. Marcus is a leader.
"Of course you've got Bruno, who has come in and you can see he's a leader because players follow him. That was the little spark we needed, from a team that should have won games to now winning games.
"And of course Harry Maguire, who's captain of the club within six months.
"Paul Pogba is an unbelievable leader, both on and off the pitch. He steps up with his world class qualities as a player but also a leader. I spent a lot of time with Paul as I had him in the reserves and it was easy to rekindle that relationship and he enjoyed it."