The 40-year-old is currently in interim charge at Old Trafford following David Moyes' sacking last month. He won his first match 4-0 over Norwich City but lost to Sunderland at Old Trafford on Saturday.
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"I can only play for United. It's black and white, and it's not about money," he told reporters.
"I've been extremely lucky in that I have only ever worked at United, but I am still a young man in relative terms in management.
"I could have another 20 to 25 years in the game – and it might not all be spent at United. If I went elsewhere it would be strange, but I can see myself doing that.
"The association I have with United will always be special – if I have to do it I'll do it, but how it will feel I don't know."
Giggs has enjoyed a glittering playing career, including 13 Premier League titles, four FA Cups and two Champions League crowns, and could make his final appearance playing at Old Trafford against Hull on Tuesday.
"It might dawn on me on Monday or Tuesday. Then I might have to put myself on the bench," he said.
"The perfect scenario would be me coming on and scoring but football doesn't work like that."