Jade Lynch, who lives in St Helens, Merseyside, told family members she was going to meet someone in the town on 26 March, but has not been seen since.
Following an appeal from her sister Stephanie, Cheshire Police say they are now following up a possible sighting in Manchester city centre.
Since the teen disappeared her social media accounts have been silent.
Stephanie Lynch, 22, said it was not like her sister to not be in contact.
She said: "All kinds of things are running through our minds. We just want to know that she is safe, that's all.
"It's not like her not to be in contact with no-one."
Det Supt Jon Betts said: "Over the past 24 hours we have received a vast amount of information from the public following the appeal for information into Jade's whereabouts.
"We are following up a number of promising lines of enquiry at various locations across the country.
"One concerns information relating to possible sightings of Jade in Manchester city centre, but this is only one of the many enquiries officers are following up."
A possible sighting of a missing 14-year-old girl is being investigated by police.