"A Pentagon statement said defence secretary James Mattis was "disappointed but understands and respects" Viola's decision", adding that it would make another recommendation soon.
Viola was one of Trump's earlier nominees, accepting Trump's offer to run his former service more than a month before the presidential inauguration.
In 2013, Viola bought the Florida Panthers NHL team for $160 million.
The 60-year-old NY native has owned the Panthers since 2015 and graduated from West Point in 1977.
"I appreciate the confidence President Trump showed in me", Viola said in a statement.
French National Assembly raided as part of Francois Fillon 'fake job' probe
However, the paper said it was unable to find proof that she had ever actually worked at the National Assembly. He has vowed to slash 500,000 public sector jobs, cut benefits and increase working time.
Donald Trump only recently announced his nominations for Secretary of the Air Force and Secretary of the Navy, according to USA Today.
Robert Speer is serving as acting Army Secretary, a step up from his previous post as assistant secretary for financial management at the service.
Viola, the founder of the electronic trading company Virtu Financial, was nominated for position in late December.
The Panthers reached the playoffs last season in their first year of ownership under Viola, and they are two points out of a playoff spot in the Eastern Conference during the current campaign. In 2003, he founded and helped fund the Combating Terrorism Center at West Point.
Leo Shane III covers Congress, Veterans Affairs and the White House for Military Times.