The 30-year-old winger is a free agent after being released West Brom at the end of last season, and is now discussing a move to the newly promoted Premier League side
The 30-year-old is a free agent following his release from Steve Clarke's side, and Palace manager Ian Holloway has highlighted the midfielder as a potential new recruit following promotion from the Championship.
Star player Wilfried Zaha has completed his move to Manchester United after spending the second half of last season on loan at Selhurst Park, while former loanee Kevin Phillips is also in talks over making his move permanent.
"We have held talks with Palace and with co-chairman Steve Parish," Thomas' agent, Tony Finnigan, told Sky Sports.
"They went well and we will be holding another round of talks, at which point we hope a deal can be finalised."
Thomas made just 10 appearances for the Baggies last season before being sent on a six-month loan to Championship side Leeds.