Boeing said earlier it had booked 1,550 gross orders and 1,432 net orders, which account for cancellations, in 2014.
After a scramble to win at least 400 orders in December, Airbus is expected to announce next week that it came ahead of its US arch-rival on both gross and net orders, the person said, asking not to be identified.
Between January and November, Airbus won 1,328 gross orders. After adjusting for cancellations, it had 1,031 net orders, leaving a gap of some 400 jets to find buyers for during December in order to remain ahead in the annual order race.
Boeing posted an industry record of 723 deliveries in 2014, retaining its title as the world's biggest jet manufacturer.
An Airbus source said earlier that it had delivered more aircraft than in 2013, when it posted a company record of 626 deliveries, but analysts say the increase will not be enough to catch up with Boeing in that category.
An Airbus spokesman declined to comment ahead of an annual news conference on January 13.
While Boeing looks certain to maintain its position as the world's largest jet manufacturer by delivering more aircraft for the third year running, the order race has been tightening after Boeing took an early lead with the launch of a 777X derivative.
Industry sources have said Airbus may be aiming for at least 1,500 orders in 2014. Airbus's 2014 tally is not expected to include a 250-plane order from India's IndiGo, which should be finalized in 2015.
It remained unclear whether Airbus would be able to book an airline order for the struggling A380 superjumbo in 2014. It has been actively looking for a home for three fully or partially completed superjumbos originally destined for Japan's Skymark Airlines, which Airbus cancelled in a row over deposits.
Turkish Airlines is one airline courted in recent months to buy or lease the world's largest passenger jet.