Reuters news agency reports the chairman of the Aena Group, Jose Manuel Vargas, explaining that he expects the conclusion of the development proposal to take place soon.
He says contracting of the work will begin as soon as the necessary permits are acquired if the Spanish operator gets the go ahead.
Vargas is also reported as saying expansion of the the airport and its runway, would require an investment of £98 million ($164.6 million).
Spain-based Aena, bought Luton airport last year, and hopes to get approval to boost the capacity to up to 18mppa.
Luton is London's fourth-biggest airport and in 2013 handled 9.7 million passengers, but has capacity for up to 12 million.
The investment would have a positive economic impact by creating jobs, Vargas adds, while shopping services would also be developed, along with transport links to the City of London financial district.
One of the biggest beneficiaries of the expansion would be budget airline easyJet, which recently secured more space at London Luton.