The former United defender believes the Norwegian has done more than enough to warrant staying in the Old Trafford hot seat.
Gary Neville has said there will be “mutiny” at Manchester United if Ole Gunnar Solskjaer does not get the full-time manager’s role.
Solskjaer became United’s interim manager in December, replacing Jose Mourinho, and has overseen a huge turnaround at Old Trafford.
The Norwegian has only lost once since taking charge, a 2-0 defeat to PSG in the Champions League, and remains unbeaten in Premier League play.
United managed a 0-0 draw against league-leading Liverpool on Sunday at Old Trafford, despite suffering four injuries during the game.
That result earned Solskjaer the record for the most points by a manager in their first 10 Premier League matches, having taken 26 of the 30 points on offer thus far.
And Neville believes that his former team-mate has done more than enough to warrant being named full-time manager, with fans at Old Trafford singing the Norwegian’s name throughout Sunday’s game.
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“I don’t think you can give it to someone else, otherwise there would be mutiny,” Neville said on Sky Sports.
“The fans were singing for him. I think it’s very close now – I can’t see the club going away from it.
“We learnt a lot about the mood of the club in that second half. Three months ago they were singing ‘attack, attack, attack’ and today there were singing Ole Gunnar Solskjaer’s name for all of the second half.
“The mood has completely transformed – the atmosphere was one of the best I’ve seen at Old Trafford for years and it was 0-0!
“If Manchester United had scored it would have been incredible.”
Manchester United midfielder Scott McTominay agreed with Neville on the feeling at the ground, saying: “I’ve never played in an atmosphere like that today.”
United dropped into fifth place with the draw, as Arsenal leapfrogged them into fourth with their 2-0 win over Southampton on Sunday.