Palace parted company with Ian Holloway last month after the 4-1 defeat to Fulham and they have been without a boss since.
Keith Millen has taken charge on a caretaker basis and managed to pick up a point against Everton last time out, although the newly-promoted side still sit at the foot of the table.
A number of men have been touted to take over at Selhurst Park with Tony Pulis and Dan Petrescu now the leading candidates.
Parish said: "Hopefully we'll get somebody announced tomorrow (Monday), but we can't be sure.
"It's still a little bit up in the air, but the most important thing is we're doing our best to get the right person."