John Textor said he tried "everything possible" to buy the remaining shares in the club, but that his bid did not receive a response.
American businessman said he will turn his efforts to selling his 45% stake in Crystal Palace "so that we can pursue a relationship with the Everton club and community".
He said there were a "significant number of parties" interested in buying his shares.
Earlier this month, Everton owner Farhad Moshiri granted a period of exclusivity to Textor.
It is true that we made an offer to buy the remaining shares of Crystal Palace, at a valuation that far exceeds levels of prior investment, TextorWrote on his , external
It is also true that our offer did not induce a response, and we believe that our Palace partners have the same desire to remain in ownership as we once did.
Textor first announced his plans to sell his staake in crystal place and an interest in buying Everton in May.
Before we decided to leave one family to join another, we did try to do everything possible to stay connected with the club and community of Crystal Palace, Textor said.
If supporters don't switch allegiances easily, owners shouldn't either.
Any deal with Everton is dependent on Textor selling his stake in Crystal Palace, as Premier League rules prohibit individuals from owning more than one team.
"We have a significant number of parties active in our process, we have received strong indications from qualified buyers, and we believe strongly that we can complete a sale of our interests to continue moving forward with the next community we hope to serve, embrace and enjoy," Textor said.
Through his company Eagle Football Holdings, the 58-year-old already has a number of stakes in other clubs, including Lyon in France, Brazilian side Botafogo and Belgian club Molenbeek.
On Thursday, French newspaper lequipe reported , external Lyon have put the majority of their squad on the transfer market in an attempt to raise funds before the end of the transfer window.
In a revealing BBC Sport interview in February, Textor called protests against his ownership by some Palace fans "nonsense" and "misguided", but said he was "in it for the long game".
No, I don't want to run [Palace] one day," he said at the time. "I don't even like running the clubs I have.
Palace chairman and co-owner Steve Parish is in charge of running the club and said earlier this month it was in a Stable Situation despite Textor's plans to sell his stake.