If the transfer is completed, Bolasie - who is originally from the Democratic Republic of Congo - would be become the second most expensive African footballer in history, behind only Sadio Mane. Mane moved from Southampton to Liverpool earlier this summer for £34 million.
Everton had already made an £18 million offer for Bolasie earlier this week, but Palace decided to hold out for much more.
Bolasie had signed a three and a half year deal with Palace last year, but it seems Everton's offer was just too tempting for the South London club. Sky says the deal should be announced by the end of this week, pending a medical.
The Congolese winger has been at Palace since 2012, making 132 appearences. He is considered to be a big part of why the Palace moved up into the Premier League in the 2013/14 season.
Everton, meanwhile, has money to burn after selling John Stones to Manchester City yesterday for £48 million. The England defender announced a six-year deal with City as part of new manager Pep Guardiola's summer spending spree. Both signings come hot on the heels of Manchester United's record-breaking purchase of Paul Pogba from Juventus, worth £89 million.
If signed soon enough, Bolasie could be in Premier League action as soon as this weekend. Everton are at home to Tottenham on August 13.