Cork is a major doubt for the start of the Premier League season after injuring his ankle in a 1-1 draw at Bristol City last night.
Saints boss Nigel Adkins said: "Unfortunately we've lost Jack Cork by the look of it.
"He's got his ankle all strapped up now.
"We will have to wait and assess but it looks as though he's gone over on his ankle.
"That's not ideal because it's his first period of time in pre-season and we wanted to get more from him but it looks like he's going to have a spell on the sidelines now."