The 24-year-old, who joined the Eagles from Bristol City in 2012, has 18 months remaining on his current deal at Selhurst Park.
Bolasie's agent John Sorzano has hinted that a deal could be finalised soon.
He told Sky Sports News: "We are in talks with Crystal Palace. They want him to extend his deal and if all goes according to plan Yannick will sign his extension."
Palace have reportedly turned down an approach for Bolasie from Fiorentina this week.