The contractor bought the site back in 2008 for around £14m.
Since that time Balfour is reported to have invested almost £30m in the site, but passenger numbers have dropped over the years.
Balfour decided to put the airport up for sale a month ago as part of a plan to raise cash from offloading assets.
A spokesman for the airport said: “We regret to announce that no agreement has been reached to secure the future of operations at Blackpool Airport.
“The airport operation has been making a loss for a number of years and unfortunately there is no option for the company other than to close.
“The airport will remain open to the public until 15 October 2014 and we will endeavour to maintain operations as normal until this date, after which time commercial flights will cease.”
The decision ends the contractors brief foray into airports.
In June 2013, Balfour jettisoned its 60% stake in Exeter Airport after paying Devon County Council £60m for its stake in 2007 at a time when traffic through the airport was taking off, almost tripling during the previous five years.