Former Chelsea boss Mourinho, who succeeded Van Gaal, has worked with Faria in his six previous managerial jobs.
“You have got to have, in your assistant, someone you have trusted all your life,” said Ferguson.
“When I came to United, I brought Archie Knox because he was a valuable person for me. I trusted him 100%. Jose Mourinho has had his assistant for years and, quite rightly, has stuck by his own man.
“If Jose hadn’t had an assistant, I know he would have taken Ryan.”
Giggs left United after failing to reach an agreement with the club over an alternative role.
He has passed all of his coaching badges, had a four-game spell as caretaker boss when David Moyes was sacked at the end of the 2013-14 season and had already been linked with other clubs before his exit was confirmed.
Ferguson feels the Welshman has the attributes to deal with the demands faced by the modern manager.
He wants Giggs to “be himself” and make sure he picks the right club to join.
“I think he is ready to manage and he has a lot of quality,” said Ferguson. “He doesn’t want to spoil that quality by going to a club where it is sacking a manager every two minutes.”
Ferguson nurtured Giggs from before he joined United, spending so much time at his house persuading the then 13-year-old to leave Manchester City that the winger’s mother Lynne started offering to make his tea.
From giving the Cardiff-born player his debut at 17, to his own retirement in 2013, they shared 13 Premier League title successes, two Champions League wins, four FA Cup triumphs and four League Cup successes.
Ferguson was confident Giggs would be a great player the moment he saw him play.
“You knew right away… the way he ran over the ground,” said Ferguson, who was responsible for all but 22 of Giggs’ club-record 963 appearances.
“I referred to it like a cocker spaniel chasing a piece of silver paper in the wind. His feet never seemed to touch the ground.”