Giggs won 13 Premier League titles as a player for United and managed them for four matches on an interim basis following the sacking of David Moyes in 2014.
"I was enjoying a bit of travelling and I got a call off Swansea and I met them a couple of times," Giggs told ITV on Saturday.
"In the end there was just mixed messages from the football side and the ownership side of the club. I just felt their ambitions did not really match mine so it didn't quite work out."
The 42-year-old Welshman, who also worked as assistant to former United boss Louis van Gaal, added that he had "an underwhelming interview for the post".
Swansea, who are 17th in the league standings on four points from their opening seven games, travel to Arsenal on Oct. 15.
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)
