The 30-year-old winger is a free agent after parting company with West Bromwich Albion.
After four years at the Hawthorns, the former Charlton winger now looks as if he is on his way back to the capital.
Palace boss Ian Holloway is looking to bolster his squad with Premier League quality ahead of the new season and Thomas fits the bill.
Thomas's agent Tony Finnigan, himself a former Palace player, confirmed to Sky Sports that talks have begun.
"We have held talks with Palace and with co-chairman Steve Parish," Finnigan confirmed.
"They went well and we will be holding another round of talks, at which point we hope a deal can be finalised."