Both players are out of contract and could join the Italian side on a free transfer, according to The Daily Mirror.
Roma have been keeping tabs on Gallas for several months and are ready to make a move.
The Italian side face competition from clubs such as West Ham, Everton, Fulham, Wigan, Blackburn, Celtic and Rangers for Ledley.
Ledley has been offered a new £20,000-a-week deal by Cardiff.
