Jeter also gave a firm endorsement for right fielder Brian Anderson to be the National League Rookie of the Year Award winner.
Speaking with reporters during the Marlins' series finale against the Cardinals, Jeter was asked if the organization hoped to retain Realmuto long term.
"He's one of the best all-around catchers in baseball," Jeter said. "Of course, I don't ever like to talk about specific players, in terms of their futures, but he's a guy we'd love to have long term."
As for Anderson, Jeter said: "He should be at the top of the list when anyone talks about Rookie of the Year. That's the bottom line. What he's been able to do since Day 1 here with this organization, and the consistency that he's shown, people don't realize he's a third baseman playing right field. That's not easy to do."
Anderson is up against tough competition, which will include Nationals outfielder Juan Soto and Braves outfielder Ronald Acuna Jr.
The Marlins view Anderson and Realmuto as building blocks.
Realmuto will be up for his first year of arbitration this winter. If he is not signed to an extension, the 27-year-old will not be eligible for free agency until the 2021 season.
Realmuto is enjoying his finest big league season and has become the face of the franchise, as well as a first-time All-Star.
"I don't think anyone deserves it as much as he does," Jeter said. "When you talk about players sometimes down in Miami, I'm finding out they don't get noticed as much as players in other organizations.
"J.T., the way he's been able to improve, year in and year out, especially this year, he's really taken some strides offensively, and even more so defensively. I think a lot of times we forget about his defense. He's someone who consistently continues to improve."
In his first season as Marlins CEO, Jeter repeated the organization is building from the ground up. That starts with the Minor Leagues.
Over the past few days, Miami's top four selections in this June's MLB Draft were promoted. Outfielder Connor Scott, shortstop Osiris Johnson and catcher Will Banfield -- three high school picks -- were brought up to Class A Greensboro. Outfielder Tristan Pompey went from Greensboro to Class A Advanced Jupiter.
"We've said since Day 1 we want athletes in this organization," Jeter said. "We've drafted great athletes up the middle, catchers, shortstops, center field, pitchers who are athletic. That's how you win games, putting the best athletes on the field. We'll continue to do that. We have a ways to go."
Still, at the big league level, the Marlins are in last place, although they've been competitive most of the season.
"No one is happy with what's happened up until this point, but we are headed in that direction," Jeter said.