Neville was Valencia boss for four months (Dec. 2015 to March 2016) in his only previous managerial appointment, and the former right-back has settled back into his role as a Sky Sports pundit since.
Former team-mate Ole Gunnar Solskjaer is at the Old Trafford helm, but Neville said in a recent Twitter Q&A that he "would run a mile" even if a vacancy opened up:
The ex-defender also said "that call isn't coming," suggesting he's aware there would likely be a long list of potential managerial fits before he received the call.
Marcus Rashford converted a penalty in the eighth minute and provided the only goal when United edged Leicester City 1-0 at Old Trafford on Saturday.
Statistician Orbinho illustrated how United have come to rely more on spot-kicks to clinch results under Solskjaer:
That was the club's second win in five matches this season and their first victory since hammering Chelsea 4-0 on the opening weekend.
Solskjaer spoke to Sky Sports after the game and acknowledged there was plenty of room for improvement:
It also brought an end to United's run of three games without a win, with the club already seven points off Premier League leaders Liverpool and looking unlikely to challenge for the title.
Neville spoke to Sky Sports during the international break and said United's recent stagnation is all the more frustrating when one considers the glory years they enjoyed under Sir Alex Ferguson:
“There is an element of frustration from United fans because of where the club have been.
“There's still that recent history of big success under Sir Alex Ferguson, but there's been six or seven years now since that. There's now an element of frustration building, real frustration, that they are not on the right track.
“I think they are on the right track because the first thing United have to do, they have to have a group of people in that changing room that want to be there. Forget how talented they are."
The former full-back has been humble enough to admit his short stint with Los Che was a mistake in hindsight:
United won the UEFA Europa League and the Carabao Cup under Jose Mourinho in the 2016-17 season. They finished as Premier League runners-up to rivals Manchester City the following campaign (19 points behind) and lost 1-0 to Chelsea in that season's FA Cup final.
The club has gone two successive seasons without winning a major trophy for the first time in 30 years, and Neville concedes he's not the manager they need to end the duck.
United begin their UEFA Europa League campaign at home to Kazakh outfit Astana on Thursday.