But if he were to sign a long-term contract extension to remain in pinstripes, there is a strong case to make it official.
There hasn't been a Yankees captain since Derek Jeter, who held the title from June 2003 through 2014, the final season of his Hall of Fame career.
In Yankees history, there have been 15 players officially designated as team captain, a list that includes Lou Gehrig, Thurman Munson and Don Mattingly.
Jeter had the longest tenure as Yankees captain.
And there wasn't expected to be another dynamic player with such Jeter-esque qualities for a long time.
Yet, in 2017, Judge quickly established his qualifications when he won the AL Rookie of the Year and finished second in the MVP voting during his 52-homer season.
Asked recently about Judge's merit as his successor as Yankees captain, Jeter provided a judicial response.
"To be fair, you find out that answer by talking to his teammates,'' Jeter said. "I watch from afar and he's a very impressive individual. Just talking to him, he's impressive.
"But to get a fair assessment of that, you just talk to his teammates. And saying that, everyone speaks glowing of him.''
So, when could it happen for Judge?
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If he's locked up to a long-term deal, there could be a suggestion from ownership that Judge be named the team's captain.
Key Yankees veterans, starting with Gerrit Cole and Giancarlo Stanton, would likely be asked for their input prior to approaching Judge with the offer of being designated as Yankees captain.
That could all take place during spring training, with a formal introduction of Judge's new Yankees title on Opening Day at the Stadium, March 30.
This article originally appeared on NorthJersey.com: Could Aaron Judge be named Yankees' next captain?