The clubs have discussed a possible loan move for the Brazil-born Spaniard, who ultimately has his heart set on a return to Atlético Madrid.
But that can not happen for six months while his former club serve a transfer ban.
Replacing the Belgian’s 25 Premier League goals and six assists from last season is next to impossible.
Toffees manager Ronaldo Koeman is prepared to give youngster Dominic Calvert-Lewin a chance but he is too raw to be the main man.
The same applies to summer signing Sandro Ramírez, as his front-line option for the whole season.
Koeman wants Costa too and when asked about the proposed deal, he said: “I have always said there will be a warm welcome for every good player here and he is a good player.”
And while Chelsea boss Antonio Conte deems Costa not fit for purpose at Stamford Bridge, he can’t just stay on strike at home in Brazil before going back to Atléti in the January window.
He also needs to play regular football before then to keep his place in the Spain World Cup squad.
So, while a Costa loan move to Everton sounds improbable at first hearing, it is not as daft as one might think.
And as there is such a strong possibility it could happen ahead of Thursday’s summer transfer deadline it is worth exploring further the pros and cons of a deal.
The gain for Everton is obvious for he is one of the few players who guarantees goals. He has had three successful years in west London, following his switch from Spain in 2014.
In 120 appearances he has scored 58 goals and racked up assists to the tune of 24. Importantly, he also scores when it matters.
It begs the question why Chelsea and Conte would want such a brilliant player out.
The problem stems from last Christmas when Costa’s head was turned by reports of a £25m-a-year contract offer from Chinese club Tianjin Quanjian.
That led to Conte briefly dropping his star striker from the side, only to successfully bring him back into the fold as Costa went on to help win the second title of what looks like his brief stay at the club.
That perceived lack of loyalty from Costa, however, was too much for Conte to bear, though it is possible the Italian coach and his bosses were thinking they should cash in while they can on a player who will be 29 in October.
The position became untenable when Costa came out with this story about a costly text he had received from the Blues boss.
He said: “Antonio Conte has told me by message. Conte said he did not count on me for next season. It’s a shame, I’ve already forwarded the message to Chelsea people to decide. But it is clear that the coach does not count on me and does not want me there. You have to find a team.”
And, in Everton, he has found one that wants him.
A downside for the Liverpool club is he is probably not going to be match fit for a month or so and they will need to find a permanent deal in the winter window when it is notoriously difficult to sign big players.
But Koeman and co. do not have much wriggle room so late in the window and this transfer represents the perfect short-term solution for all four parties: Chelsea, Everton, Atlético Madrid and the player himself.
That is a rare win-win-win-win situation in football.