Norwegian Solskjaer, who spent 11 years at United as a striker between 1996 and 2007 and scored 126 goals, was given the caretaker role until the end of the season on Wednesday following the sacking of Jose Mourinho.
Twenty-time English champions United have suffered their worst start to a season for 28 years and are 19 points off leaders Liverpool and 11 points behind fourth-placed Chelsea.
"For United, a top-four finish under Solskjaer is going to be difficult -- though not impossible," Berbatov, who spent four years at Old Trafford from 2008, told Betfair.
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"If he achieves it he'll surely get to manage the club beyond this season.
"Catching up with Chelsea would be phenomenal and would show the board that they have a guy who can transform the team and harness the talent at Old Trafford."
Berbatov, who won two league titles with United, said that Solskjaer had earned his chance after steering Molde to two Norwegian titles in 2011 and 2012.
"There are only a few 'chosen ones' who start off at big clubs," Berbatov said. "Pep Guardiola and Zinedine Zidane both had lesser roles at Barcelona and Real Madrid before taking the reins to great success -- but Ole earned this opportunity through his good work in Norway and coaching at United.
"Even if he doesn't get Champions League qualification he can still be a success based on what they show on and off the pitch. It's good for Ole that he has Mike Phelan and Michael Carrick alongside him as that offers continuity for players."
Tottenham Hotspur manager Mauricio Pochettino has emerged as United's most likely target for a permanent manager but Bulgarian Berbatov, who left Tottenham to join United, hopes the Argentine stays in north London.
"I switched from White Hart Lane to Old Trafford and it's the same for a manager as a player," Berbatov said. "You ask yourself 'Am I going to miss my chance? Am I going to pass on my big break?'
"But if you look around realistically at the moment, it's a funny situation as Spurs are 13 points clear of United in the table and in a better position than their rivals up north.
For me, I want Solskjaer to stay at United and Pochettino to stay at Spurs. They are young and in a good place right now." (Reporting by Shrivathsa Sridhar in Bengaluru; editing by Martyn Herman)
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