Neville was recruited as a coach at Old Trafford under former boss David Moyes, while Butt was promoted to the backroom staff to assist Ryan Giggs when the Welshman took over on an interim basis following the Scotman's axe.
Netherlands manager Van Gaal has already appointed Giggs as his number two for the new campaign, but it remains to be seen whether Neville and Butt will be part of the new era.
According to BBC Sport, both former players will be informed by the club regarding their United futures at some point next week when Van Gaal is expected to begin work at his new club following the World Cup in Brazil.
"Football moves on and sometimes you have to move on," Neville is quoted as saying. "My future will probably be resolved in the next five days.
"I am speaking with the chief executive. There is no fall-out. If I am not involved [as a coach], I am sure I will be able to play a part in it in other ways."