Other names in the potential exchange were not revealed.
The talks between New York and Los Angeles did not get far and were described as "the lightest of flirtations."
"Teams talk all the time about a wide range of players, from their best to their least accomplished," added Olney.
Judge, who turned 29 on Monday, is eligible for free agency in 2023 and is making $10.175 million this season.
The two-time All-Star has been tremendous for the Yankees when healthy, hitting .271/.389/.553 with 123 home runs and 276 RBIs in 443 games.
However, injuries have limited Judge's playing time. The California native has appeared in more than 102 games only once throughout his career.