Martial penned a new five-year contract on Thursday that will keep him at the club until 2024.
Martial scored in Solskjaer's opening game at Cardiff and then broadcasted his effectiveness off the bench when he sealed Man Utd's win at Arsenal in the FA Cup.
Solskjaer is unbeaten in nine matches - eight of which he has won - since taking over in a caretaker capacity from Jose Mourinho at Old Trafford in December.
"We all knew his qualities, I remember talking to [Dimitar] Berbatov, who played at Monaco with him, and he was raving". He seems to be getting better and better as time goes on.
Solskjaer played alongside the Portugal global for much of his spell at United and feels Martial can replicate the success enjoyed by the now Juventus forward.
Though not involved in negotiations, the Norwegian hopes Martial's display of commitment will show others the way.
He appears to be playing with more confidence now, and Solskjaer sees the new contract as a sign of the club's faith in the forward.
"You can talk about Cristiano's career, what he's made, how he's got there and all the fantastic players we've got, so I sat down with Anthony and he wants to be a part of this and we believe the club have got a top player there".
Ole Gunnar Solskjaer has backed Anthony Martial to follow in Cristiano Ronaldo's footsteps and become a world class player at Manchester United, using the example to persuade the Frenchman to stay. I made my career here, it was easy to sell the club to Anthony but he knows what we're capable of. "We believe in him because he's got fantastic potential".
Martial was fined by Mourinho after failing to return to the club's pre-season tour of the United States following the birth of his second child and was on the fringes of the side in the early weeks of the campaign.
"We had good discussions, obviously he got injured so we spoke about that but nothing's confirmed so I can't say more, really". "This is the flawless club for Anthony to progress his development as a top-class forward and we are all delighted he has signed a long-term deal".
However, according to The Sun, Solskjaer will be handed the full-time job if he manages to lead the team past PSG, with the first leg of their knockout-round tie due to take place at Old Trafford on February 12.