Giggs retired from international football in 2007 with 64 caps for Wales, having never played in a European Championship or World Cup finals.
Asked where an Olympic medal would rank among all the medals he has won with United, Giggs told the Sunday Mirror: "Right at the top. Up there, I don't like to prioritise medals because every single one means something special.
"Of course, this would be different because you never thought you'd be competing in an Olympics, so to win a gold medal would be special.
"Not playing in a major tournament would have been a missing piece in my career, had I not had this chance, no doubt. My career for my country has been the total opposite to my club career - I've been so successful with United but not so with Wales.
"I would always watch the other lads, especially those I grew up with, Becks, Butty, Nev, Scholesy, go away to international tournaments and I would wish that I could do the same.
"Unfortunately, I never got the chance. But now I've got the chance and even in the first few days together I've seen things that I haven't seen in my career. It's been an eye-opener and really enjoyable as well."