Oulare was rushed to hospital on Tuesday morning complaining of chest pains and breathing difficulties, but doctors have yet to pinpoint the exact problem.
The 29-year-old only joined the Potteries' outfit at the end of December, and made his debut as a substitute in Sunday's draw at Northampton.
His Second Division career is now on hold as the tests continue, although he is described as being in a 'comfortable' position in the North Staffordshire Hospital.
A blood clot on his right lung had initially been suspected as being the problem, but Stoke physio Stefan Stefansson admits doctors are keeping an open mind.
Stefansson said: "He has undergone ventilation scans, but they have so far proved inconclusive, so doctors are keeping him under observation for further tests. Thrombosis remains a possibility, but basically they are ruling nothing out at this stage.
"I have worked in a hospital for five years and I can tell you he was very distressed and in a lot of trouble.
"His breathing was very shallow and at one stage I really thought he was passing away. It was a very unpleasant experience.
"But he was conscious throughout and gradually got better throughout the day."
Meanwhile, Swede Mattias Ostberg played for the reserves in their clash with Walsall.
Ostberg, who playes in Sweden for Norkopping, has been offered the chance to impress Stoke boss Gudjon Thordarson with a trial at the Brittania Stadium.
