Isabel Gayther, 21, was last seen at about 11:30 GMT on Christmas Eve.
Posts on her Facebook account in response to media coverage state she is "not missing" and has not come to harm.
The Met, which earlier said it was "concerned" for Miss Gayther, said it was aware of the messages but had not been able to speak to her.
A spokesman said an investigation continued, "with the aim of establishing that she is safe and well".
Miss Gayther lives in halls of residence in New Cross, south-east London.
She also has family in Oxford.
