Betting is said to have been suspended on the former Stoke City boss leaving Selhurst Park, with Palace co-chairman Steve Parish also refusing to confirm that he will remain in charge for the club's Premier League opener.
The Eagles travel to the Emirates Stadium on Saturday afternoon to face Arsenal and their chances of gaining a result would be thrown into chaos should their manager leave just a day or so before the beginning of the campaign.
The uncertainty is said to stem from clashes between Parish and Pulis over new signings.
Palace have signed three new players this summer, with Liverpool's Martin Kelly set to be announced as a fourth, though 56-year-old Pulis is reportedly frustrated at what he perceives to be a lack of transfer activity at Selhurst Park.
Reports claim the two have been at loggerheads for months and that their disagreements may come to a head before the start of the new season.
Pulis only took over at Crystal Palace last term, when former boss Ian Holloway stepped down, suggesting he was not the best man for the job of keeping the club in the Premier League.