Yes, there are multiple flights from Thailand to Palermo for under ฿25,181. The cheapest flight booked recently is on Air France for just ฿23,324, but on average you can expect to pay ฿23,355.
There are no direct flights from Thailand to Palermo, but Cheapflights can provide you with all the information you need to find the fastest route with the fewest stops.
Departing from Thailand to Palermo will take you 42h 35m.
Flying on Air France is currently your cheapest option to Palermo, with prices starting at ฿23,324.