Saturday’s defeat by Villa was the second consecutive match they have lost after being 2-0 ahead.
Dyche, who kept Everton up last season despite the club receiving deductions totalling eight points for breaching Premier League financial rules, said after the match: “I didn’t come into this season thinking everything was solved because we finished strong last season, absolutely not.
“There’s massive challenges ahead we need to correct and that’s my job and my responsibility.”
Crystal Palace co-owner Textor has been granted a period of exclusivity as he aims to buy Blues owner Farhad Moshiri’s majority stake in the club.
Any deal is dependent on the American selling his 45% stake in Palace as Premier League rules prohibit individuals from owning more than one team.
The 58-year-old said he has received two “good bids” for his Palace stake and has a contract with Moshiri to complete a deal for Everton by a deadline of 30 November.