Solskjaer has won 14 of his 19 games in charge of the Red Devils since replacing Jose Mourinho on an interim basis in December.
United have rejoined the top-four battle under the Norwegian and progressed to the quarter-finals of the Champions League, but the club are yet to make a decision on who will occupy the Old Trafford hot seat next season.
And Matic, whose own form has drastically improved since the change of manager, has called on the board to hand Solskjaer the job full-time.
“I think he is a great manager,” Matic toldESPN. “But you have to say also that with Mike [Phelan], Michael [Carrick] and Kieran [McKenna] they work very well together. They work as a team. It is not only Ole.
“There are people behind him who help us. I will be happy if he stays, and I hope he will.”
United, who are currently two points behind Arsenal in the final Champions League qualification spot, face Watford in the Premier League this weekend.