The Norwegian replaced Jose Mourinho after the Portuguese was sacked in December and has managed to turn around the club's performances, notably improving the mood at Carrington and finding himself as favourite to succeed Mourinho on a permanent basis.
Neville, a former teammate of Solskjaer, told Norwegian television channel TV2 on Wednesday night that he expects that to be made official during the upcoming international break.
When asked if Solskjaer will be the next permanent manager, Neville said: "He will," before joking "he'll probably be the king of Norway, the president of Norway and the prime minister of Norway as well."
Neville added: "I can't believe what's happened. I thought, when he first came in, it was just to reconnect the club with the fans, the players and get everyone happy.
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"He's a safe pair of hands, someone that the club could rely upon to give good information to the boardroom about what the players are like. And then they would appoint the best manager in the world.
"Ole's results are Premier League title-winning results. The form guide says it all. The performances are very good, the fans are loving it, it's been a sensational three months.
"I think Ole Gunnar Solskjaer will get given the job. The right time for me was always mid-March to the end of March, and that's when the international break is.
"I'll be surprised if Ole Gunnar Solskjaer is not awarded the job in the international break in the next couple of weeks."
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