Earlier Wednesday, the New York Post reported that Loria is being considered for the position, with White House Chief of Staff Reince Priebus pushing for his nomination.
"Our family has been friends with Jeff Loria for over 30 years, been in business together, and even owned a AAA baseball team together," Kushner's son-in-law, Joseph Meyer, said in a statement. "Although the Kushners have made substantial progress in discussions for us to purchase the Marlins, recent reports suggest that Mr. Loria will soon be nominated by the President to be Ambassador to France. If that is true, we do not want this unrelated transaction to complicate that process and will not pursue it. The Kushners remain interested in purchasing a team and would love to buy the Marlins at another time."
Charles Kushner's son Jared is the senior adviser to Trump and is married to the president's daughter Ivanka.
Last week, Forbes and The Associated Press reported that Loria has a preliminary agreement to sell the team for about $1.6 billion to a New York businessman, but the deal could fall through because the final purchase price hasn't been determined.
While noting that a potential sale had a long way to go, ESPN reported that Charles Kushner was part of the potential purchase group, although it was not known if he was the primary bidder.
The New York Times, meanwhile, reported Kushner's other son, Josh, as well as Meyer have "pursued the Marlins for several months."
Major League Baseball, in a statement last Thursday, said "the Commissioner's Office has not heard directly or indirectly of any conversation involving Charles Kushner."