Solskjaer is yet to lose a domestic game since being appointed Manchester United interim boss in December.
The Norwegian has led the Red Devils to fourth in the Premier League and the quarter-finals of the FA Cup.
And Neville, speaking ahead of the Champions League last-16 second leg against Paris Saint-Germain on Tuesday, is convinced his former team-mate will be given the job full time imminently.
The pundit admits he is shocked at how well Solskjaer has done in temporary charge and expected him to only be a short-term solution following the sacking of Jose Mourinho.
And he expects a permanent appointment to be announced during the upcoming international break.
“He will [be the next permanent manager],” Gary Neville said on Norwegian TV channel Viasport.
“He’ll probably be the King of Norway, the President of Norway, the Prime Minister of Norway as well.
“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, get everybody happy.
“A safe pair of hands, someone that the club can rely upon to give good information to the boardroom about what the players are like, and then they will appoint the best manager in the world.
“Ole’s results are Premier League-winning title 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 during the international break in the next couple of weeks.”
