Palace saw Dougie Freedman leave for Bolton Wanderers last month and his former No.2 Lennie Lawrence also made the journey to the Reebok Stadium on Thursday.
That has left Curtis Fleming in caretaker charge ahead of Saturday's Championship game against Blackburn Rovers, but Holloway could be appointed before that fixture.
Reports have suggested that Holloway could be presented as Palace's new boss on Friday, although Parish says there is still work to be done to finalise an appointment.
"An approach has been made but it's far from done," said Parish.
Holloway had also been linked with the now-filled roles at Blackburn, Burnley and Ipswich Town in recent weeks, but has emerged as the odds-on favourite to take charge at Palace.
He has been at the Blackpool helm since 2009 and led the club to promotion to the Premier League during his first season.
The Seasiders missed out on a return to the top flight in May after losing to West Ham in the play-off final and made a positive start to the current campaign.
However, a run of just one win in seven matches has seen Blackpool slip to 12th in the table, six points behind Palace, who are in fourth.
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