Star slugger Judge opted to enter free agency, turning down a seven-year contract with the Yankees before the season started.
His stock has risen since then, with Judge having scored a record-breaking 62 home runs in the regular season and racked up 131 RBIs.
Yankees general manager Cashman on Friday gave little away when asked about the possibility of Judge returning next season.
"When you make these commitments on players, you know he's a fan favourite," Cashman said during a press conference.
"He interacts with our fans extremely well. He's respected within that clubhouse, handles his business as good as you possibly can. He's an elite performer – among the game's best, if not the best player. With all that being said, those are the types of players you want to retain and have as long as you possibly can."
Cashman added: "As George Steinbrenner [the former Yankees owner] said, he puts fannies in the seats. People want to go watch that guy play, and you want to put great teams on the field that they want to come here to watch compete and win.
"Certain individual players transcend the team and everything stops when they're at the bat or they have the ball in their hand. He's one of those types of talents."
Cashman, whose future is also unclear after his contract expired, has no issue with Judge biding his time.
"[Judge is] going to dictate the dance steps to his free agency and he has worked extremely hard to earn this position, so we'll see how this plays out," Cashman said. "It can tie you up a little bit along the way, but he's not the only guy that we're needing to deal with.
"He's the most important, but if he came in here today and said, 'Oh, man, I'm signing up, let's go,' there's still a lot of work to be done."
Aaron Boone spoke to Judge in his office after the Yankees missed out on the World Series when they were subjected to a clean sweep by the Houston Astros.
The Yankees boss reiterated that he hopes Judge will be back to lead the team.
He said: "Of course I hope he's back and a Yankee forever. I can't think of a better guy that you want to be leading your team and leading your organisation, and hopefully that all works out.
"But my conversations with him now are just communicating with him through the winter and hoping that it works out. But obviously, that's above me."