The Robins did not disclose which club were interested in the 25-year-old, but according to Sky Sports News, it is Wigan Athletic who made the two offers.
A Bristol City statement read: "Bristol City Football Club can confirm it has received two undisclosed bids from an unnamed club for winger Albert Adomah.
"Both offers have been rejected. The club plans to make no further comment at this time."
Adomah has scored 17 goals in 131 appearances for the League One outfit.