Both players are now free agents.
Shaw - who has spent time at first, second, and third base - produced two stellar seasons for the Brewers in 2017 and '18, but he lost his starting job during a dismal 2019 campaign. The 29-year-old hit a career-worst .157/.281/.270 with seven homers and 16 RBIs in just 86 games, and he spent a large part of the year at Triple-A San Antonio.
Brewers general manager David Stearns said that he had negotiations with Shaw's agent throughout the day, but the sides were unable to reach an agreement before the 8 p.m. ET non-tender deadline, according to Tom Haudricourt of the Milwaukee Journal Sentinel.
"Travis was such a key component of (the) team for multiple years," Stearns said. "A big reason why we were able to become a competitive franchise again. We just couldn't line up (on a deal) today."
Nelson was one of Milwaukee's top pitchers two years ago before getting injured while running the bases. After missing all of 2018, he finally made it back to the majors in 2019 but struggled, posting a 6.95 ERA and 1.91 WHIP with 26 strikeouts and 17 walks in only 22 innings.
Milwaukee did sign shortstop Orlando Arcia and outfielder Ben Gamel to one-year deals, avoiding arbitration with both players, while also tendering contracts to pitchers Josh Hader, Corey Knebel, and Brent Suter.
Despite the five non-tenders and the recent losses of Yasmani Grandal and Mike Moustakas in free agency, Stearns has no plans to tear down a Brewers team that's aiming for a third straight playoff appearance.
"We intend on being competitive once again next year," Stearns said, according to Haudricourt. "We think we have a quality team and will continue to complement and add to that team throughout the rest of the offseason. We've got a lot of offseason left."