The Germany international has been stuck on the bench at PSG all season and, with the World Cup on the horizon, he knows he needs to be playing regularly again to force his way into Joachim Low's squad for Russia 2018.
The Sun claim Palace, currently in 18th in the Premier League, would like to sign Trapp in January to bolster their chances of avoiding relegation.
The former Eintracht Frankfurt stopper has made just one Ligue 1 start this season and, despite keeping a clean sheet against Troyes last weekend, was dropped again for PSG's defeat to Strasbourg on Friday.
"Of course I've said that you have to play regularly to attend the World Cup, and I've never seen a coach nominating someone who does not play," said Trapp last week.
"This is not the time to talk about my future, we have six or seven games to go and we'll see what happens during the winter break."