Neville played under Moyes at West Ham and worked with the Scotsman as a coach at United.
The former England star has outlined what he wants to see from Moyes at the London Stadium.
Neville told beIN SPORTS about Moyes: “I want to see his eyeballs popping out like I saw at Everton. It was like David Moyes ‘I will take on the world’. That’s what I want to see.”
Meanwhile, West Ham winger Michail Antonio has outlined how things are at the moment under Moyes.
The former Sunderland boss was recently appointed the Hammers boss following the departure of Slaven Bilic.
Antonio told BT Sport about life under Moyes at West Ham: “Things are looking good to be honest. He has come in, he is quite intense.
"Everything is quite different. He is out there, he is standing with the boys, he is taking training himself, he is very involved. I see positive things.”
West Ham are struggling at the moment and are in danger of getting relegated to the Championship at the end of the season.
The Hammers are currently third from bottom in the league table with just nine points from 11matches.
Allen wrote in The Daily Mail: “I’m looking forward to seeing a fitter, more organised, disciplined team of men under Moyes and with some new recruits in January, they will definitely stay up.”
West Ham will take on Watford away from home at Vicarage Road in the Premier League on Sunday.