Everton boss Sean Dyche. (Steve Paston/PA)
The Friedkin Group reached an agreement to buy Farhad Moshiri's majority stake in the club in September but the process has yet to be concluded.
That has left Dyche in virtual limbo regarding planning for the January transfer window, while striker Dominic Calvert-Lewin is among a host of players whose deals expire in the summer.
On a possible new contract for the 27-year-old, Dyche told a press conference: "The situation is an ongoing one where we'll have to wait and see. He's got his things to think about, the club have.
"Obviously possibly new ownership, still not there yet, we'll wait and see, that might play its part. All those things have to combine. He's working hard, we want him to continue working hard.
"I've been down this road many times with players and I'm sure the club have as well so we'll manage it the best we can and see what comes next.
"Obviously it's not been so helpful with the ownership changeover because you've got to wait and see what the new owners want to do and what their situation is should they come and take the club, which is looking very possible like it's going to happen. But, until it's done, it's not done."
Everton return to action against Arsenal on Saturday following the postponement of last weekend's Merseyside derby because of the effects of Storm Darragh.
"We wanted to play the game, but safety had to play its part," said Dyche. "I was here in the morning and the wind was horrendous, to be honest, so they had to call it and that was a blow for everyone, I think, because everyone was gearing up for it. We park that and we move forwards."
Dyche has been boosted for the trip to the Emirates by an easing injury list.
Defender Michael Keane is available again after a minor knee problem while Seamus Coleman, Armando Broja, Youssef Chermiti, Nathan Patterson and Jake O'Brien took part in a game at Finch Farm earlier this week.
On-loan Chelsea forward Broja played the final few minutes of the 4-0 Premier League victory over Wolves last week, and Dyche said: "He'll be around it.
"I only got him on to give him a feel of it. There's a long way to go yet but he's showing he wants to be competitive in our group and competitive in the games he plays. It was a little cameo but hopefully he gets more and builds what he's doing here."