In court documents unsealed Monday, Amazon said it is looking to depose "individuals who were instrumental" in the JEDI selection process, including Dana Deasy, the Defense Department's chief information officer, Defense Secretary Mark Esper and former Defense Secretary James Mattis.

The Department of Defense (DoD) awarded the $10 billion JEDI contract to Microsoft last October. The project is meant to modernize the DoD's cloud infrastructure and connect different divisions within the agency, which currently has over 500 separate clouds. Amazon quickly challenged the decision and filed a lawsuit. The company claims Trump's "personal vendetta" and instruction to "screw Amazon" cost it the contract.

In a statement provided to CNBC, an Amazon Web Service spokesperson said: