Balfour Beatty, which bought the facility in 2008, put it up for sale a month ago to end its involvement in running regional airports.
Only three airlines – Jet2.com, Citywing and Aer Lingus Regional – run regular scheduled flights from the Lancashire airport.
A statement from the airport said that if no sale agreement was reached by October 7 then the last flights would be on October 15.
“On 28 August 2014, we announced our intention to find a buyer for the airport operating company,” it said.
“The airport operations have been making a loss for a number of years and we are currently exploring a number of options in an attempt to secure the future of the airport.
We regretfully confirm that if no agreement can be reached before 7 October 2014 which ensures the viability of its operations, then it is likely that the airport operations will close.
“In this event, we expect that the last commercial flights will take place on Wednesday 15 October 2014.
“We apologise for the uncertainty this will cause over the coming weeks and we recommend that any affected passengers contact their airline to confirm travel arrangements.”
Jet2.com said: “We have been made aware today, of the notice on the Blackpool airport website, stating that the airport may close on 15 October.
“It is our intention to continue operating flights as normal from Blackpool airport and we are currently working on our contingency plans, to ensure that all our customers get to and from their destinations.
“In the event that it is confirmed that Blackpool Airport will close, we will be contacting our Jet2.com and Jet2holidays customers to make alternative flight arrangements.”
Sourced from Travel Weekly