The New York Post reported Wednesday that Loria, a New York art dealer, is likely to be the next French ambassador. The report named him as one of four people selected by White House chief of staff Reince Priebus for top diplomatic posts.
Loria is a longtime major contributor to the Republican National Committee, which Priebus led until taking the job with Trump. Fundraising records show Loria gave $125,000 last fall jointly to the Trump campaign and RNC.
It has long been a presidential tradition to reward generous political donors with plum ambassadorships.
The statement from the Kushners was the first public confirmation of their negotiations with Loria.
"Our family has been friends with Jeff Loria for over 30 years, been in business together, and even owned a Triple-A baseball team together," the statement said, referring to an Oklahoma City club.
Joshua Kushner, 31, is a New York City businessman and investor and part of the real estate family that also includes Jared Kushner, Trump's son-in-law and adviser.
Marlins officials haven't commented. Team president David Samson said he will speak Friday about the status of sale negotiations.
Other parties are also interested in buying the Marlins, and Loria might reopen negotiations with them.
Jared Kushner, who is married to Ivanka Trump, is not believed to part of the recent effort to the buy team. Neither is the Kushners' father, Charles, who ran the family real estate firm until he went to prison for tax evasion, making illegal campaign contributions and witness intimidation.
The Marlins, who last won the World Series in 2003, began spring training this week amid the news of a possible sale. Manager Don Mattingly said the ongoing developments won't be a distraction.
"Above my pay grade," Mattingly said Thursday. "I don't worry about things I can't control. It's the same with this ballclub. When you play professionally, you know how to cut out distractions."
Mattingly was the Los Angeles Dodgers' manager when Frank McCourt sold that team after it filed for bankruptcy.
"That was more of a soap opera, for sure," Mattingly said. "But even though there was a lot of talk about it and a lot of noise about it, it really didn't change anything I was trying to do. It has nothing to do with what we at field level are trying to do. And it's not like we're getting updates on what's going on. We don't really know."