Spanish newspaper AS claim new Palace manager Frank de Boer could use his connections with Barcelona in order to strike a deal for the former Ajax goalkeeper, and are expected to make Barcelona an offer.
Cillessen, 28, endured a difficult spell at Barcelona following his move from Dutch giants Ajax last summer, making just 10 appearances in all competitions and keeping only three clean sheets.
The Hammers could be in the market for a new goalkeeper in the coming months, as Slaven Bilic looks to mould a side capable of challenging the top end of the Premier League and potentially qualifying for the Europa League.
This Is Futbol considers three reasons why Cillessen would be the perfect signing for the east London outfit as they look to put behind their cheerless 2016-17 campaign.
Here are those three reasons, with a reported move for a proven goalkeeper set to be shelved due to a sky-high asking price: