Scholes would reportedly be willing to drop his role as a TV pundit for ITV and BT Sport for a coaching position at Man United.
The 41-year-old has been a vocal critic of van Gaal, who oversaw a 2-1 defeat against FC Midtjylland in the Europa League on Thursday.
Sources close to United are said to be baffled that Scholes has not been used at Old Trafford amid claims that the club are losing their identity.
Scholes is reportedly indifferent about working in the media and is keen to move into coaching and management as soon as possible.
United had no fight, no poise and no hunger against FC Midtjylland, something that rarely happened while Scholes was part of the team. His inclusion in the set-up would be a boost but it is unlikely that it will happen as long as van Gaal is still in charge.