Jeter, who played in his third minor league rehab game with Triple-A Scranton/Wilkes-Barre on Monday night, said he'd like to return to the Yankees "as soon as possible."
When asked if he'd made that clear to Cashman, Jeter said, "What do you think? Yeah, but I get it. It's not like I don't understand why I'm here. I know I have to play some games, so just make the most of it while I'm here, and get into some games, and like I said, hopefully get out of here soon."
Manager Joe Girardi on Sunday all but ruled out Jeter returning to the Yankees before the All-Star break. The Yankees resume play on July 19 against the Boston Red Sox after the break, which begins on July 14.
"What's my pat answer? He's ready when he's ready," Girardi said. "I think what you have to do is you have to see how he's moving around, how he's responding physically from playing every day. You have to build him up. He has to be able to play more than five innings once every three days. So I mean we'll go through this week, I'm sure, and we'll make an evaluation."
Jeter, though, said before Monday's game that he's made a push to speed up the timetable. Jeter is expected to take the day off Tuesday and resume his rehab assignment Wednesday with Scranton/Wilkes-Barre.
"I'm trying to push to get there today, but I don't think I can make it today. So it's whenever they say," Jeter said before the RailRiders' game against Rochester. "Really, I don't know what else to say. I'd like to be there now, but I'm not, so as soon as I'm allowed to get up there, I'll get up there."
Jeter broke his ankle on Oct. 13 and had surgery. He played five spring training games, but a new break was discovered April 18. He has not played in a regular-season game this year.
In his two minor league games before Monday's tilt, Jeter went a combined 1-for-4 with three walks. He played five innings at shortstop on Saturday and played DH on Sunday. On Monday, he went 0-for-2 with a walk and a run scored in five innings.
"I feel good. I felt fine. There's been no issues whatsoever," Jeter said after the game, a 6-3 RailRiders win. "I had to run a lot and everything felt good."
Jeter tested his ankle on the basepaths, scoring from second on a single and going from first to third in the first inning after he reached on an error. He also made a charging play at shortstop in the first and fielded a throw from catcher J.R. Murphy at second and tagged out the Rochester runner.
He had to move laterally on the play, so it seemed to be a good test of his ankle.
"You never know what's going to come up, but I feel as though I've tested it," Jeter said after the game.
He is not worried about playing a full nine-inning game before returning to the Bronx. He likened his rehab stint to spring training.
"If you think about it, in spring training, I don't think I've played nine innings in a spring training game in 15 years. So I don't think necessarily there's a big difference between seven innings, nine innings," Jeter said. "I don't know what their plan is, but I don't see that being an obstacle. I think it's more of just day-to-day, as opposed to how long in a day."
Jeter said he feels stiffness in his ankle occasionally, but defined it as "nothing out of the ordinary."
"Some days it's going to be stiff. But that goes away. From what I understand, I'm going to have days like that forever," he said.
He added that he wants to be back with the Yankees "as soon as possible."
"I feel good. So whenever they let me get out of here," Jeter said. "But I understand I have to play some games, so we'll see. But as soon as I can, I want to go."
Ian Begley is a regular contributor to ESPNNewYork.com.