Pulis admitted after his side's defeat to Chelsea on Saturday that his future in the West Midlands is uncertain, and The Mirror has said that Northern Ireland coach Michael O'Neill could replace the Welshman.
O'Neill was fast-tracked by Sunderland as a potential recruit at the Stadium of Light following the departure of Simon Grayson, but he turned the opportunity down.
Pulis met West Brom chairman Tony Williams after the 4-0 defeat and spoke in his press conference about the situation.
"The important thing is that the decision is right for the club," he said. "That decision won't be mine - that's one for the owners. I am disappointed we have not got the result we wanted for them as much as anybody else."
The Scottish FA has been given permission to talk to O'Neill, but the report says that the Scots would be unlikely to compete with Premier League wages.