It is claimed that Pulis' name was in the frame for the role, and although not ruled out by Bilbao, it is believed that other managers are preferred.
Former Valencia boss Ernesto Valverde, who has coached Bilbao before, and current youth boss Jose Ángel Ziganda are the favourites for the role.
Sources told Sky Sports: "Nothing is decided on the coach, but we are managing some names.
"The club have received offers from some foreign names but normally we desire a coach that knows La Liga and the style of Athletic."
Bilbao are looking for a new coach after they surprisingly opted not to renew the contract of Marcelo Bielsa.