The Blues are set to table an improved bid of £50m for the 21-year-old attacker, who still has three years left to run on his contract at Goodison Park.
Everton rejected a £45m offer from Chelsea on Monday having previously turned down a £40m bid over the weekend.
The English youngster has been identified as an exciting prospect who can develop into a star player under Chelsea head coach Thomas Tuchel.
The West Londoners are now set to test the Toffees’ resolve with a new-and-improved £50m bid for the youngster.
Chelsea have already spent more than £150m this summer on five new additions, including Raheem Sterling from Manchester City for around £47.5m.
However, the Stamford Bridge outfit remains active in the current transfer market and are looking to strengthen their options in the final third following the departures of both Romelu Lukaku and Timo Werner.
Gordon joined Everton’s academy in 2012 before making his professional debut for the Merseyside club in December 2017.
The winger contributed seven goals in 40 appearances for Everton across all competitions last season.