Everton paid out a club-record £25m plus £5m in add-ons to land goalkeeper Jordan Pickford from Sunderland last week.
Ronald Koeman has also splashed £23.6m on Ajax midfielder Davy Klaassen, taking his summer spending over £50m already.
And according to The Sun, Koeman wants to break the bank with a big-money move for striker Dembele.
Everton are preparing to lose Romelu Lukaku ahead of next season, with Chelsea and Manchester United interested.
The Toffees are expected to demand a deal worth around £80m for their star striker and could reinvest funds in Dembele.
The 20-year-old shone for Celtic under Brendan Rodgers last season following his £400,000 move from Fulham.
Dembele scored 32 goals as the Scottish giants won all three domestic honours, sparking a late deadline day bid from Chelsea in January.
Chelsea, Arsenal, Liverpool, Manchester United, Borussia Dortmund, Bayern Munich, Barcelona, Juventus and AC Milan have all expressed an interest in the France Under-21 international.
But Everton could be set to trump their rivals with a bid worth over £30m and by offering the player guaranteed first-team football.
Rodgers and Celtic are desperate to keep Dembele in Scotland for another year but would find it hard to turn down a huge offer.
Last summer Dembele’s agent and mentor Momadi Fofana convinced him to move to Scotland despite bigger offers elsewhere.
Fofana insists he wants to help his client develop as a footballer rather than jump at the first big offer he gets.