The 21-year-old is said to have held talks with the Premier League champions, but ended up completing a switch to Bayer Leverkusen from Hamburger SV.
"Manchester wanted Sonny, they had a strong interest and had contacted HSV. We already talked," his agent told Bild.
"Their interest honoured him, but Leverkusen made the better impression. It's the ideal interim stage for his career right now."
Son has scored once in four appearances for Leverkusen so far this season.