Solskjaer, in charge until the end of the season following the sacking of Jose Mourinho, has won his first five games since taking on the role.
“If United keep going like this – and there's no reason why they will stop performing – the job will surely be his," said Berbatov to the Mirror.
“He's doing a great job. By the end of the season, as long as they keep playing like this, they should give him the job whether or not they finish in the top four.
“If they don't, I'm sure that another Premier League team will give him the job. He's making his name once again in the top-flight and it's great for him.
“When a club legend becomes your manager, he automatically gets the attention of the players, purely because he had been there and done that.
“When you are in the position of Ole, having scored so many goals and won so many trophies, he gets the attention.
“He doesn't need to yell or scream to prove anything, he just gets it.
“From that point on, he needs to show them that they need to trust him, that he knows what he's doing and, judging by the results and the way they play, it's obviously working."