The 25-year-old winger is believed to be a target for relegated Wigan and Premier League new boys Crystal Palace.
Adomah has just one year left on his current contract at Ashton Gate but the club are determined not to let their star man leave on the cheap.
A statement from City 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 scored seven goals in 46 appearances for City last season.