"I'm not speaking for Joe, but I think if you're good at what you do, you'll have opportunities to stay," Cashman said. "He's definitely going to have that. We're going to give him a real good reason to stay. He's earned that."
The 2013 season marked Girardi's sixth at the helm of the Yankees. Over that span, Girardi has compiled a 564-408 regular-season record, winning one World Series, but also missing the playoffs twice.
Girardi said during the Yankees' season-ending series in Houston that he has loved his time with the organization, but that he has not made up his mind about managing in 2014.
"It comes down to family," Girardi said on Sunday. "They are first, and whatever is best for the group of us -- not one individual, not me or just my wife or just one of my children -- whatever is best for us as a group, that's what we'll decide to do.
"And that's something I've put some thought into and I'm going to have to think about a lot of the next few days. But that's a decision that we'll sit down and make and decide what's best."
He has been mentioned in media reports as a candidate for the Cubs' managerial vacancy, as Chicago parted ways with Dale Sveum this week, but Girardi said on Sunday that his connections to the Windy City are not as strong as they once were.
Asked if he would grant the Cubs permission to speak with Girardi, Cashman declined to comment.
"We can't control what other options or interests may be out there," Cashman said. "If you're good at what you do, people are going to have some interest. You can't predict the future on that; you can only control your side of it. I feel we hired a good one.
"He's been a world-champion player for us, a coach, a broadcaster, and obviously a world-champion manager. We've benefited from having him and we'd like to do that going forward. We'll have to stay tuned and see how it plays out."
Cashman said that if Girardi returns, the Yankees would also be interested in retaining the entire coaching staff: bench coach Tony Pena, hitting coach Kevin Long, pitching coach Larry Rothschild, infield coach Mick Kelleher and outfield coach Rob Thomson.
"They're not technically free agents until Oct. 31," Cashman said. "If Girardi comes back, I would like to have our coaches back, and I think Girardi feels the same way. But ultimately, because of the way the process needs to work, the manager has to be decided first and then you can focus on the coaches."
Though the Yankees posted only 85 victories in 2013, their lowest total in a full 162-game season since 1992, Cashman said that Girardi has been "consistently tremendous" in making the most of his roster and keeping the club motivated.
"This year was unique in a lot of different ways and he was able to still maintain that leadership, keep these guys hungry and motivated and not give up," Cashman said. "They never did. I never saw that. Thumbs up. I thought he did a great job, him and his staff."