Speaking ahead of Liverpool v Manchester United on Sky Sports on Sunday, Neville he still has big doubts over Pogba's long-term future at United, after his agent Mino Raiola suggested in December that his star client wanted to leave the club.
It was the latest interjection from Raiola, who has previously hinted the French World Cup winner was not happy at United, but Neville believes his future is on ice for the next six months.
"Paul Pogba does feel like he should be playing in the best team in Europe, I think he genuinely believes he believes he should be competing for the best trophies," United legend Neville told us.
"He's confident in his own ability, and I think the reason you've seen him step up in the last couple of weeks is, obviously, the team's playing better, I think they are a little bit more in sync with each other.
"He's playing alongside some seriously good players there: Cavani, Martial, Rashford, Greenwood, Fernandes are really good players. In any team in the country, they're decent players.
"Pogba is playing in a team that is growing in confidence, he's growing in confidence, the maturity in his performances is growing in the last few weeks."
Neville suggests this surge in form from Pogba may be a temporary revival, as he predicts he will again be looking to leave United this summer, as he believes the signing of Donny van de Beek last summer was completed with possible departures in mind.
"Coronavirus and the economic troubles of football have meant Pogba has now decided this season he is going to stay at Manchester United," he continued.
"I just think the right thing to do now is probably not to talk about Pogba's future and think that it will be reviewed after the European Championship in the summer.
"Manchester United, Paul Pogba, Mino Raiola, Ole Gunnar Solskjaer, I'm sure are going to sit down and review that at the end of the season, I'm sure it's not going to be for now.
"The Van de Beek signing is an interesting one - I still can't get my head around it, it's almost as if that signing was sort of done in anticipation of one of the others leaving because Van de Beek has just sat on the bench for the last few months and he cost £40m.
"I think that Manchester United are preparing for someone leaving. Maybe Pogba could leave, so they've already got Van de Beek in to maybe assume that role, but I think now, the way Paul Pogba's playing and the way Manchester United's season is going, there's no one going to come in in January and buy Paul Pogba, I don't think Manchester United would let him go."
Neville also praised Solskjaer's management, as he shrugged off the comments from Raiola and has found a way to get the best out of an unsettled player.
"The way Ole handled the Raiola comments was masterful," he added. "He knew he was going to have him at least until the end of the season, he's sort of poured cold water over it and he's now got him performing and proven to have handled that situation really well.
"So I would say Ole Gunnar Solskjaer deserves real credit for how he's dealt with Pogba in the last couple of months. It could have easily blown up, going out of Europe and his agent making those comments but he handled it brilliantly and his man-management of that situation incredibly well."
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