Pearce joined Derby last summer on a free transfer from Reading, ending a a 14-year association with Royals.
The 27-year-old came through the ranks at Reading and played for them in the Premier League and made over 200 appearances for the club.
Pearce has found first-team opportunities hard to come back at Derby under Paul Clement since his arrival, with his only appearances coming in two outings in the Capital One Cup and the FA Cup.
Pearce is keen to go out on loan in search of regular first-team football as he wants to boost his chances of making the Republic of Ireland squad for this summer's Euro 2016 finals.
Bristol City are desperate to bolster their squad during this month's transfer window as they look climb to safety from the wrong end of the Championship table.
The Robins have one of the worst defensive records in the league and they know they need to shore up their defence if they are to stay up.
Despite being without a manager following the sacking of Steve Cotterill, Bristol City are ready to push through a move for Pearce to bolster their squad.