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, he already has a number of stakes in other clubs, including Lyon in France, Brazilian side Botafogo and Belgian club Molenbeek.
On Thursday, French newspaper L’Equipe 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.