The Premier League giants are believed to be on the final leg of identifying and appointing a new manager for next season.
Erik ten Hag is believed to be the frontrunner to become the next Manchester United boss and it has emerged he was interviewed by the club on Monday.
The Dutchman has a €5m release clause in his Ajax contract, which is unlikely to be an issue if Manchester United decide they want him.
Manchester United are insistent that the process is far from complete and they will conduct more interviews, with Julen Lopetegui, Mauricio Pochettino and Luis Enrique still in the running.
But Neville believes that since the formal interview process has begun, Manchester United could be in a position to make a decision and announcement on a new manager sooner than expected.
The former Red Devil said on Twitter: “Reports Ten Hag has been interviewed this week.
“If formal interviews have started and with it being such a public process I would expect a new manager announcement within a week or so.”
There are suggestions that Manchester United could decide on the new manager before the end of the current month.
