The Airbus Group subsidiary beat its 2013 peak of 626 deliveries but is expected to remain behind rival Boeing, which is due to issue annual data later on Tuesday.
The source also said the European company is expecting "one of the best years ever for Airbus" in orders, but it remained unclear whether this would be enough to close a gap with Boeing on winning new business in the first 11 months of the year.
In 2013, Airbus won a record of 1,503 net orders after adjusting for cancellations, but lagged on deliveries.
An Airbus spokesman declined to comment on orders or deliveries ahead of an annual news conference on Jan 13.
Airbus is officially targeting "about the same" level of deliveries as in 2013 and is already guaranteed to reach its other objective of winning net orders that exceed deliveries.
Boeing is targeting 715 to 725 deliveries and is expected to remain ahead of Airbus in deliveries for the third year running after resolving earlier delays to its 787 Dreamliner.
Airbus delivered the first of its competing A350 jets last month and is expected to increase output sharply by 2018.
Deliveries are widely watched by investors since that is when plane-makers get paid.
Some industry analysts are focusing in particular, this year, on whether Boeing can surpass Airbus in deliveries of profitable single-aisle jets for the first time since 2002.
Deliveries of the Boeing 737 medium-haul jets outpaced the Airbus A320 family between January and November, but December may have been an unusually busy month for Airbus.
According to delivery-tracking website Hamburg Finkenwerder News, Airbus delivered as many as 60 A320-family jets from three separate plants in December, a record for the month.
The traditional order race between plane giants is harder to predict. Boeing has been ahead for most of the year, but much depends on whether Airbus finalizes a 250-plane order for India's IndiGo.
Airbus was hit by the cancellation of 70 A350 jets from Emirates last year, but has a tradition of announcing last-minute surprises after a push to close deals over the New Year.
Airbus won 1,328 total orders between January and November. After adjusting for cancellations, it had 1,031 net orders.
By Dec 16, the latest period for which data is available, Boeing posted 1,423 gross orders. Net orders stood at 1,317.
(Tim Hepher - Reuters)