And former Manchester United defender Neville has clearly been very impressed by Pogba's recent upturn in performances for the Red Devils this season.
Mourinho won the League Cup and UEFA Europa League in his first season in charge, though United finished sixth in the Premier League.
Reports earlier in the season placed major question marks over Mourinho's long-term commitment to United.
However, Shaw has now completed 90 minutes in six matches in the space of a month, and Mourinho has claimed that there are few better left-backs than the England worldwide.
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Dyche will be boosted by the timely return of Scott Arfield for the visit of United after the midfielder suffered a hamstring strain in the New Year's Day defeat by Liverpool, but striker Jon Walters has been ruled out for up to eight weeks following knee surgery.
'Physically much better, mentally much stronger, tactically understanding the game much better and what we need in different phases and circumstances.
"So every player you then phone about has miraculously gone considerably up in value because they'll look and say it doesn't mean he's as good but he must be somewhere nearer on a sliding scale", he added.
Ahead of the weekend's action, Zlatan Ibrahimovic and Eric Bailly remain sidelined for United, while Daley Blind will also miss the fixture with a "small problem".
The trip to Turf Moor is a chance for United to cut Manchester City's lead at the top of the table to nine points with Pep Guardiola's side hosting Newcastle at the Etihad Stadium in Saturday's late kick-off.