Ronald Koeman revealed the midfielder has now suffered an ankle injury, which he picked up playing for the under-21s side on Monday, keeping him out for a further two to three weeks.
Another summer signing, Caulker, will also miss the Saints first home game due to a sinus infection.
The news comes as the latest injury blow to Koeman's plans following Fraser Forster, Florin Gardos, and Ryan Bertrand's absences.
"We have some difficulties with injuries," said Koeman. "Everybody knows the situation of Fraser [and] everybody knows the situation of Florin.
"Jordy Clasie was back [but] he played last Monday and got an ankle injury and he will be out for the next two to three weeks.
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Jordy Clasie ix expected to be out for another two to three weeks says Koeman
"We have Steven Caulker, he has an infection in the sinus. He was in hospital for two days. He's not in the physical state to be involved at the weekend but we hope that he will be available next Thursday [against Midtjylland in the Europa League].
"Ryan Bertrand is still not available. Maybe in two weeks he will be part of the training sessions."
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