Airbus will probably not increase production of its narrow-body A320 airplane in the near future due to supply chain limitations, Aviation Week reported Friday.

Airbus, a subsidiary of Leiden, Netherlands-based EADS N.V. (Paris: EAD), presently builds 40 single-aisle jets per month and has considered increasing the rate to 44 a month, according to the Aviation Week report. However, COO for Customers John Leahy has now said that he tends to doubt an increase in production will take place.

However, in the long-term, production rates are expected to rise and demand for the airplane is so high that 44 per month in 2017 or 2018 may not be enough to feed demand, according to Aviation Week.

A new, more fuel-efficient version of the plane, the A320neo, is expected to come to market in 2015. Malaysia's AirAsia Bhd (PINK: AIABF) is negotiating a $4 billion deal with Airbus for 50 A320 airplanes in the meantime, Reuters reported. The A320 competes with The Boeing Company (NYSEP: BA) 737.

EADS N.V. (Paris: EAD) shares were down 2.36 percent Friday to €27.33 ($34.36).