Newly appointed U.S. Secretary of Defense Mark Esper is reviewing a controversial multi-year cloud-computing contract, a spokesperson said.

The Joint Enterprise Defense Infrastructure deal, which could be worth up to $10 billion for services rendered over as many as 10 years, could go to either Amazon or Microsoft. Those two companies are the top players in the market for cloud infrastructure that companies and governments can use to host applications and store data. The JEDI deal could cement them even more as being ready for the most formidable computing workloads.

"Secretary Esper is committed to ensuring our warfighters have the best capabilities, including Artificial Intelligence, to remain the most lethal force in the world, while safeguarding taxpayer dollars, Defense spokeswoman Elissa Smith told CNBC on Thursday. "Keeping his promise to Members of Congress and the American public, Secretary Esper is looking at the Joint Enterprise Defense Infrastructure (JEDI) program. No decision will be made on the program until he has completed his examination."

The Pentagon had said before that an award could come as soon as August.

The announcement comes after President Trump said last month that he had received complaints from companies about the process. Trump said companies conveyed that the specifications of the contract favored Amazon, according to Bloomberg. IBM and Oracle have been out of the running for the contract for months.

Secretary Esper was sworn in last month, replacing for Jim Mattis. In a meeting with reporters last week he said the JEDI deal is something he wanted to take a "hard look at."

-- CNBC's Amanda Macias and Ryan Ruggiero contributed to this report.