Dellenger added that additional details of the phone call "remain private" and that neither the White House nor LSU responded to messages seeking further information.
While Dellenger noted Orgeron is registered as an independent, he attended a fundraiser for Louisiana's Democratic Gov. John Bel Edwards in April.
Upon winning re-election in November by defeating Republican challenger Eddie Rispone, Edwards credited LSU's success with indirectly helping his campaign.
"It is an easier state to govern when the Saints and LSU are winning," he said to the New York Times' Rick Rojas and Jeremy Alford. "People are just in a better mood."
Trump held a rally for Rispone days before the election, and The Advocate's Elizabeth Crisp wrote he "has developed a close relationship with several politicians with LSU ties, including House GOP Whip Steve Scalise."
Trump was also on hand for one of LSU's biggest wins, making the trip to Tuscaloosa when the Tigers defeated Alabama 46-41.
According to Dellenger, it's unclear whether Trump will attended the College Football National Championship on Jan. 13, when LSU will face off with Clemson in pursuit of its fourth national title.