The Norwegian took over from sacked manager Jose Mourinho on a caretaker basis in December and has transformed the club’s form, leading them to the Champions League quarter-finals and fifth place in the Premier League.
However, his future in the role remains shrouded in uncertainty, with his current deal due to expire at the end of the season.
“Talking as a former player I am sure the current playing staff at the club would welcome some clarity on Solskjaer's status at the club,” former Red Devils striker Berbatov told Betfair.
“It's tiring to have so much change in the managerial position. A club needs that stability at the top. For a team that didn't change manager for 25 years to have so much churn in such an important role suggests they don't know what they're doing.
“With all the work he has done I don't think it would be fair to him or the players if they don't announce that he is going to stay in charge.
“Ole was able to raise the spirit, the team, everything at the club. He was the guy who took responsibility in a difficult situation. Purely on what he achieved so far he deserves an extension. He has earned it.
“He is young for a manager, an ex-United player - it's the best combination for the club to build for the future.”
Berbatov also insisted there is no need for United fans to be concerned over Paul Pogba’s comments about Real Madrid this week.
The France midfielder said on international duty that the Spanish club “is a dream for anyone”, but Berbatov believes the quotes shouldn’t be taken too seriously.
“Paul Pogba is rarely too far away from the headlines but I'm not concerned about his Real Madrid quotes this week," he said.
“I supported lots of other teams when I played for United because I was a fan of good football. I admired clubs like Real Madrid, Juventus, Bayern Munich.
“I don't think there's anything to worry about here. We live in a world where you can say what you want and I can imagine the words being taken out of context.
“Paul will be a United player for a long time, as long as he and the club want to be together.
“I remember Paul coming to play with the first team, training with us. He was just enjoying being in Manchester and was good friends with the first team and when you're happy you're settled.
“He caused a stir in training straightaway. He was tall, athletic, would get the ball from me, intercept it and get on my nerves. I knew I had to take this guy seriously because he had something.
"You could see from the beginning that he had technical ability, vision of the game, where to position himself and now you can see the result - he is one of the best in the world.”
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