Manchester United need someone to help them in the transfer market, according to former Tottenham and Liverpool director of football Damien Comolli.
The club missed out on numerous targets before signing Everton's Marouane Fellaini for £27.5m on deadline day.
"If there's a club who needs a director of football it's United," said Comolli.
"It would ease the process for both individuals."
Moyes was also unsuccessful earlier in the summer when Barcelona midfielder Cesc Fabregas stayed at the Nou Camp and midfielder Thiago Alacantara opted to join German side Bayern Munich when he left the Spanish champions.
United's former manager Sir Alex Ferguson left the club at the end of last season, while chief executive David Gill also moved on from Old Trafford in June.
However, Comolli, who was in charge of transfer affairs at Tottenham from 2005 to 2008 and at Liverpool from 2010 to 2012, said a director of football would have eased the pressure on Moyes and Woodward.
"David only joined on 1 July which was quite late," added Comolli on BBC Radio 5 live.
"The issue for Manchester United is that the two most important people at the club in Sir Alex and David Gill left their positions and new people came in for their first transfer window.
"For some reason the club weren't prepared or they didn't think it would be that difficult and they ended up in a difficult situation."