The 20-year-old forward is a hot property in Brazil, and was linked to Liverpool in the past.
And the Daily Mail claims Evanilson is someone who Palace boss Roy Hodgson admires and would like to bring to the Premier League.
Palace are also trying to complete a deal for Jeremie Boga, a former Chelsea player.
The 23-year-old would be a possible replacement for Wilfried Zaha, who wants to leave Palace.
Palace hope to have a signing completed before the Premier League begins next weekend.