Mr. Loria was a six-figure donor to Mr. Trump's joint fund-raising effort with the Republican National Committee during the campaign, and a job in the administration has been a priority of the White House chief of staff, Reince Priebus.
He continued: "If that is true, we do not want this unrelated transaction to complicate that process and will not pursue it".
In a statement Wednesday night from Jared Kushner's brother-in-law, Joseph Meyer, the family made clear that it would not proceed with the deal.
Loria was in headlines last week after it was reported he had an agreement in place to sell the Marlins for $1.6 billion.
In a statement provided to The Post, Meyer said, "Our family has been friends with Jeff Loria for over 30 years, been in business together, and even owned a AAA baseball team together". The Kushner family acknowledged interest Wednesday, but, in a statement, vowed to back out if Loria is appointed to avoid the perception of a quid pro quo.
Diplomacy, perhaps, according to a report from the New York Post.
Charles Kushner's son, Jared, is the senior adviser to Trump and is married to the president's daughter, Ivanka.
Officials with the Marlins have not commented, and team president David Samson is expected to address the issue on Friday.
Other parties are also interested in buying the Marlins, and Loria might reopen negotiations with them.
Loria donated $125,000 to the Trump Victory Committee a year ago, according to finance reports.
ESPN's Darren Rovell later reported real estate mogul Charles Kushner who was involved in a deal.
The potential sale of the Miami Marlins could be on hold due to current owner Jeffrey Loria's diplomatic future.