Pulis left Selhurst Park on the eve of the Premier League season amid reports of a disagreement over the club's transfer policy.
Malky Mackay had looked set to take over, but Palace pulled out of the deal after allegations of distasteful text messages sent by the Scot emerged.
Tim Sherwood claimed not to have been offered the job after an interview, and former Celtic boss Neil Lennon is currently the bookmakers' favourite to be installed.
And Parish concedes he has once again found it tough to appoint a manager, having taken over a month to replace Ian Holloway with Pulis last season.
"You read all sorts of things about how many people we've seen," Parish told the Croydon Advertiser.
"I have seen very few people, probably two, but spoken to other people about managers and doing background work and due diligence.
"It's not a revolving door of people coming in and having a chat. We have got a profile of a manager we think needs to carry the club forward based on what I've experienced over the last four years.
"Finding the right person isn't easy. A lot of managers are in jobs and they're not going to leave clubs early in the season, so it's a difficult situation."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
