The 21-year-old is keen on a move to Stamford Bridge and will now finalise personal terms ahead of a medical, although he is sidelined for several weeks with a hamstring injury.
Olise has attracted interest from a number of clubs including Manchester City but Chelsea have moved quickly in recent days to try to secure his signature.
Chelsea have spent more than £275m so far this summer -- including breaking the British transfer record to sign Moisés Caicedo from Brighton in a deal worth up to £115m -- but are continuing their policy of signing young talent on long-term contracts.
Olise joined Palace from Reading in 2021. He scored two goals and registered 11 Premier League assists in a 2022-23 campaign which saw him voted the club's Players' Player of the Year.
The France Under-21 international would be Chelsea's eighth major summer signing if a final agreement is reached and a ninth could follow quickly after sources told ESPN that Chelsea have agreed a fee worth up to £58 million ($73.7m) with Southampton for midfielder Romeo Lavia.
As was the case with Caicedo, Chelsea are believed to be edging out Liverpool in the race to sign Lavia, who has stated a preference to join the London club.