Saints' fine start to the season is fast becoming a distant memory, with Wednesday's 3-2 home defeat to Aston Villa their third loss in succession.
Mauricio Pochettino's side are not only struggling for form but also injuries heading into Saturday's clash with City.
Wanyama and Clyne joined the growing number of absentees after being forced off against Villa.
"Victor has a hairline fracture [in his leg]," Pochettino said. "We don't know time-wise how long he is going to be because it also depends on personal recovery times.
"I hope he recovers soon. Right now, we don't know exactly when.
"Clyne made a sharp movement against Villa in the second half and received a tweak in the pelvis region."
Guly do Prado and Danny Fox are long-term absentees, while Paulo Gazzaniga will again start in goal as Artur Boruc fractured his hand last week and back-up Kelvin Davis is struggling with a side injury.
The only good news on the injury front for Saints is the return to fitness of former club record signing Gaston Ramirez, although he has not been a regular this season.
"Before the game against Chelsea, Gaston was suffering from a bad cold," Pochettino said.
"Even before the game against Aston Villa he was still recovering from that, but these past few days he has been training will. We are confident he will be fit for tomorrow."
- Sports & Recreation
- Mauricio Pochettino