Skysports.com understands Colchester have rejected two bids from an unnamed Championship club for Marc Tierney.
Tierney is expected to leave Colchester after he turned down the club's final offer of a new deal.
The 25-year-old's contract expires at the end of the season and the news has alerted a number of clubs to his possible availability in the January transfer window.
One of Tierney's suitors is thought to have tabled two bids for the full-back only to have seen their offers rebuffed by the League One outfit.
It remains to be seen if the interested club will come back with a third offer for Tierney as they look to prise the former Oldham man away from Colchester.