Cork is expected to be sidelined for a few weeks after suffering an ankle injury in last weekend’s win at Crystal Palace.
Wanyama was due to replace him in the line-up this Saturday, but he sustained a knock in training on Wednesday.
The Kenyan was recently out of action for around two months, following a hairline fracture in his leg, and his latest injury is in the same area.
Saints manager Mauricio Pochettino said: “Regarding Victor Wanyama, he had a knock in the same region as the previous injury.
“He does have some pain right there in the same region. We need to evaluate more than anything his fitness in terms of playing tomorrow.”
Pochettino did say, however, that Cork, Wanyama and Kelvin Davis, who has a troublesome hamstring issue, were the three players likely to miss out.
James Ward-Prowse appears the obvious candidate to come into midfield, in the absence of Cork and Wanyama.