Her family said they were devastated, saying Olivia was "an extremely beautiful and talented girl" who loved drama and music.
The hospital recently suspended visiting to try to reduce the risk of patients and staff catching flu.
The trust has begun an investigation to determine the cause of Olivia's death.
It said in a statement: "Wirral University Teaching Hospital NHS Foundation Trust can confirm that a 17-year-old person admitted to Arrowe Park Hospital died over the weekend period.
"The cause of death has not yet been confirmed. Because of patient confidentiality the trust is not in a position to release any further details."
Olivia Rae Clee-Barnett Swine Flu
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