President Donald Trump speaks to reporters after arriving at Pitt-Greenville Airport before heading to a campaign rally at Williams Arena in Greenville, North Carolina, July 17, 2019.

President Donald Trump said Thursday that he's seriously considering looking at a Pentagon contract that's said to be worth up to $10 billion for Microsoft or Amazon.

"I never had something where more people are complaining," Trump said, adding that he's going to take a close look at it.

"We're getting tremendous complaints from other companies," Trump said in a press pool at the White House during a meeting with the prime minister of The Netherlands. "Some of the greatest companies in the world are complaining about it." He named Microsoft, Oracle and IBM.

Since April, Microsoft and Amazon have been the only remaining competitors for the contract after IBM and Oracle were ruled out by the Defense Department. The contract, known as JEDI, is viewed as a marquee deal for the company that ultimately wins it, particularly as Microsoft and Amazon are aggressively pursuing government work for their expanding cloud units.

While Trump didn't cite Amazon CEO Jeff Bezos by name Thursday, the billionaire executive has been a constant source of frustration for the president. Bezos owns The Washington Post, which Trump regularly criticizes for its coverage of his administration. Trump also has gone after Amazon repeatedly for, as he claims, not paying its fair share of taxes and ripping off the U.S. Post Office.

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The Joint Enterprise Defense Infrastructure, or JEDI, contract was originally supposed to be awarded in September 2018. The cloud computing deal could be announced as early as next month, the Pentagon told CNBC.

The Pentagon did not respond to CNBC's request for comment regarding Trump's statements. A Microsoft representative declined to comment and a spokesperson for AWS didn't respond to an inquiry.

IBM told CNBC, "IBM has long raised serious concerns about the structure of the JEDI procurement. We continue to believe that the Department of Defense and our men and women in uniform would be best served by a multi-cloud strategy."

AWS and Microsoft are the only companies that meet the minimum requirements for the contract, Defense Department spokesperson Elissa Smith told CNBC in April. Business from the CIA in the U.S. has been a big boon for AWS.

Last week, Oracle lost a court challenge in which it contended that the contract was tainted by conflicts of interest.

WATCH: President Trump says he will look closely at contract with Pentagon