The Dutchman recommended the current Wales boss take the reins from him once he had completed three years in Manchester. However, Van Gaal spent only two seasons in Manchester before being shown the door in 2016.
Giggs was the former Ajax, Barcelona and Bayern Munich coach's assistant at United, but Van Gaal's long-term vision failed to come to fruition.
Speaking to Donald McRae of the Guardian, Giggs explained it was the veteran who said he should be his successor when asked if United gave him any assurances about his future career at the Theatre of Dreams.
No, it was more Louis [Van Gaal] who said it. You know how Louis is. He told Ed Woodward [United’s executive vice-chairman]: ‘I will be manager for three years and then Ryan will take over.’ [Giggs laughs.] Typical Louis. No one else made me any promises. I didn’t think I was ready when I finished playing but, after working with Louis, I felt more than prepared. I know it didn’t work out for United but Louis was brilliant for me because he is a teacher.
Van Gaal arrived at United after the failure of David Moyes to replace the iconic Sir Alex Ferguson at the helm.
Giggs joined the coaching staff after a brief spell as interim manager at the end of Moyes' time at Carrington.
Van Gaal's tenure was a stale period for the team. The club won the FA Cup at the end of the manager's second year, but a lack of victories in the Premier League saw United bring in Jose Mourinho.
Giggs has given his blessing to existing interim boss Ole Gunnar Solskjaer, saying his former team-mate should be given the post full-time for next season after Mourinho's sacking last December.
Per McRae, when asked if he thinks the Norwegian should be named manager at the end of the season, Giggs said: "I do. We've messed around far too long. When you've got someone who knows the club, who is tactically astute, clearly has the players and fans on board, that gives you lots of momentum. There will be bumps in the road but most fans imagine what he could do with the money that's been spent the last few years."
Giggs remains one of United's greatest legends, and the 45-year-old took control of Wales after the departure of Chris Coleman in 2018.
The Welshman could return to Old Trafford in the future, but he will need to serve a full apprenticeship in management before Woodward would think of him as a serious candidate.
Solskjaer has jumped the queue to gain his chance at United. His experiences behind the scenes at Carrington as a coach under Ferguson and his period as manager of Molde and Cardiff City have given him a strong grounding to be considered by the Red Devils board.