The Ukrainian producer of the world's largest aircraft has offered to build a plane for Donald Trump after the US president-elect said an order with Boeing Co for a new Air Force One should be scrapped.

"@realDonaldTrump May be it is better to consider #Antonov aircraft as Air Force One?," Ukrainian state-owned firm Antonov tweeted directly to Trump.

There was no immediate response from the future president, who is known for his unpredictable tweets.

Yesterday, Trump took to Twitter to criticise alleged escalating costs for a new Air Force One from Boeing, which has built planes for U.S. presidents since 1943.

"Costs are out of control, more than $4 billion. Cancel order!," he wrote.

Antonov's offer appeared to have been in jest, but new orders from the United States or elsewhere would provide a welcome boost to its fortunes.

The company, one of the Soviet Union's top aircraft producers, has produced only around twenty planes since Ukraine gained independence in 1991.

It is most famous for building the world's biggest aircraft: the Antonov-225 Mriya (Dream) cargo plane, which was designed as part of the Soviet space programme. The only one completed is still in use and can carry up to 250 tonnes over distances of up to 4,000 km (2,485 miles).

Work to manufacture a second plane was started in 1988 and never completed, but Antonov has now found a potential investor in the Aerospace Industry Corporation of China (AICC).