Murtough was in charge of the academy at Everton when Moyes was manager, but United sources say he would not be taking over from Brian McClair, who currently heads the academy set-up.
Instead, Murtough has been earmarked for a role working across a number of different areas at Old Trafford.
Murtough, 40, who has also worked at Fulham, joined the Premier League a year ago to work alongside director of youth Ged Roddy.
Meanwhile, United would not comment on reports that they want to agree a new deal with Wayne Rooney by the new year.
Rooney, whose future at United looked in doubt over the summer, has been in excellent form in this campaign and has just under two years to run on his current contract.
David Gill, Manchester United's former chief executive who is now a club director, said last month the England striker would be a offered a new contract "without doubt" if he continued his form.
United's executive vice-chairman Ed Woodward said on Thursday he believes the gap is widening between the salaries of the superstar players and those of the rank and file.
Woodward envisages the very top players continuing to be able to demand higher and higher wages but UEFA's financial fair play rules, and new regulations brought in this season by the Premier League, are bringing pressure to bear on salaries.
Woodward said: "In terms of player wages we are seeing inflation around it but we are also seeing, particularly within the Premier League, a fall in the acceleration around player wage growth.
"I think (this is) due to financial fair play rules and the rules that have been put in place in the Premier League.
"But when you look at the top end of wages, the top 10 teams in Europe or the top players, we are seeing inflation at that end. There is a bit of a mix going on and we will present a blend of that over the next three to five years."