During Holloway's final news conference as manager, Palace co-chairman Steve Parish said the club hoped to talk to Pulis, but it is understood the former Plymouth Argyle boss was initially cautious about taking the job.
It is understood he wants to bolster the squad during the January transfer window to aid Palace's fight for survival.
Summer changes cost Palace - Holloway
There were rumours Wales manager Chris Coleman could be appointed before he
committed his future to his country,
with Iain Dowie and new Middlesbrough manager Aitor Karanka also linked with the role.
Parish had also explored the possibility of appointing former Chelsea defender Dan Petrescu, who is now manager of Dinamo Moscow.
However, Petrescu said: "I have not been in talks with any club being under contract with another outfit. And I'm not set to do it in the future."
Welshman Pulis was appointed Stoke boss for a second time in 2006 and two years later led them into the top flight
after a 23-year absence.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.