The appeal was made while divers conducted a search of the Grand Union Canal after a rucksack belonging to Alice was found nearby.
However, police are insisting that at the moment it is purely a 'missing person' search.
Detective Inspector Julie Willats, leading the hunt, said Alice, 14, and her mother had been shopping on the morning of August 28 (last Thursday) and the teenager had gone for a walk in the afternoon, which was not out of the ordinary for her.
When she failed to return in the evening, the family became worried and phoned friends.
DI Willats confirmed that Alice had been suffering from anorexia and had weighed 40kg at the time of her disappearance.
Police are concerned she "may have collapsed" but insisted the river search was a matter of routine.
