United are looking for a new head coach after sacking Solskjaer on Sunday and Paris Saint-Germain boss Pochettino has been tipped to take over.
Solskjaer had overseen a terrible run of results but until Saturday was being backed by the club’s hierarchy. He was then dismissed following the 4-1 humiliation at Watford.
Pochettino is believed to be willing to depart the Ligue 1 side to take over at United.
But former midfielder Scholes believes Pochettino should have been appointed in 2018.
The Argentine was still managing Tottenham when United sacked Jose Mourinho three months into the 2018/19 season.
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Pochettino was widely linked by Solskjaer ultimately won the job, initially on a caretaker basis. At the time, Scholes called for Pochettino’s appointment.
“Pochettino’s the man. If he wants the job then I think it’s his,” Scholes told BBC Radio 5 Live in 2018.
“He carries himself brilliantly with the media and with his team. He promotes young players and most importantly he wins a lot of football matches.
“I know people say he’s got a great team at Tottenham. He has.
“But can he ever really win the league with Tottenham? I’m not sure he can.
He continued: “Confidence is obviously very low and he’s going to need some new players, there’s no doubt about that.
“Especially if Pochettino comes in, he wants his players to play football and play with confidence so he’ll need a couple of centre-halves who can play football and can play out from the back.
“I think he’ll need a midfield player, possibly a centre-forward so you’re looking at maybe three or four players. Pochettino, if he comes, will bring his experience with what he’s done at Tottenham as well.
“He could make a big difference to this team.”