Sky Sports football expert Guilleme Balague says Quique Sanchez Flores has been given until Friday to make up his mind over becoming the new Stoke manager.
Balague, a well-respected Spanish journalist, claims the current Espanyol boss has already met with the club's board over a potential deal.
Stoke have reportedly offered the former Watford boss a five-year contract to take over from Mark Hughes.
Balague was quoted: "They (Stoke) want an answer tomorrow. Quique Sanchez Flores has not said yes but will answer tomorrow. He will either give them an immediate yes or he will stay at Espanyol.
"My instinct is that the proposal is so interesting plus the fact that Espanyol have not kept their promise from when Quique first arrived suggests to me that will announce his depature from Espanyol".
Flores has 18 months left until his current contract expires with Espanyol.