But the deal the White House now supports will carry costs barely below the $4 billion mark.
The current Air Force One 747 jets are nearing the end of their 30-year design lifetime, and the plans for replacing them have been in the works for years. And the Air Force had already been working to reduce the cost of the program before Trump was elected.
The U.S. Air Force reached an agreement last summer to purchase two Boeing 747-8s to serve as the next Air Force Ones.
In December 2016, Trump tweeted that costs for the program were "out of control, more than $4 billion".
Sources in Pentagon and industry expect the jets to ultimately cost more than $3.9 billion - and also that Trump's unprecedented involvement will in fact save some money.
During the transition, then president-elect Trump protested against Boeing's initial asking price.
The White House said the deal would put Boeing on the hook for cost overruns.
In a statement, Boeing said that "President Trump negotiated a good deal on behalf of the American people".
"Boeing learned first, of all the defense contractors, that you have to flatter Trump, you have to give him credit for any number of things, no matter how fictitious", Aboulafia was quoted as saying. The actual deal is pegged around $3.9 billion.
The President, who has repeatedly expressed his exasperation at his aging aircraft, wanted to meet face-to-face with Muilenburg to reach the deal, two officials said. The cost question concerned the modification process - the conversion of normal jetliners into Air Force One.
The White House credited Trump's negotiations with the aircraft manufacturer for the smaller bill in the final deal. Since the cost to complete the program was listed as "continuing", Aboulafia said it could be reasonable to expect costs near or a little higher than $4 billion.
The Air Force purchased two existing 747 airframes that built for the Russian airline Transaeo, which is now defunct.