The Blues made bids of up to £45million for the England Under-21 international but have been put off by the Toffees’ valuation.
They now no longer want to bid beyond even £40m for Gordon while Everton manager Frank Lampard has claimed that Chelsea have missed their deadline to do a deal.
“He's too important a player and I think he showed his worth in the last two games,” Lampard said at after his side's 1-1 away draw at Leeds.
“And with two days now to go [until the transfer window closes], what good would it do us to do anything with Anthony? On a bigger picture than that, he is our player who we've developed and there's an affiliation with him and the fans and vice versa.
“Clearly, the interest has been there because he's a top player. And that's why we're so keen to keep him.”
The Merseyside club are now said to be negotiating a lucrative new contract for Gordon who has scored in the last two matches.
A Chelsea deal for Crystal Palace star attacker Wilfried Zaha has also been described as ‘unlikely’ by sources close to the situation.
Meanwhile, the academy’s interest in Dinamo Moscow midfielder Arsen Zakharyan has hit issues over the paying of his transfer fee.
Sanctions on the Russian economy due to the war in Ukraine are now expected to block any move for the 19-year-old to move to west London, ending any option to activate his £12.6m release clause.