According to MLB Network's Jon Morosi, the Angels are "moving closer to a decision," but it isn't yet known who is favored to land the job.
Mike Scioscia stepped down as the Angels manager at the conclusion of the 2018 regular season, marking the end of a 19-year run in that position.
L.A. has finished 80-82 in consecutive seasons and hasn't reached the playoffs since 2014.
The 49-year-old Ausmus, like Scioscia, is a former MLB catcher who played for the San Diego Padres, Detroit Tigers, Houston Astros and Los Angeles Dodgers. He was a one-time All-Star and three-time Gold Glove award winner.
Ausmus served as the Tigers manager from 2014 until his dismissal in 2017.
Although Detroit went 90-72 and reached the playoffs during his first year at the helm, they went just 64-98 in 2017, and he finished with a 314-332 record overall.
Chavez, 40, was primarily a third baseman during an MLB career that spanned 17 seasons with the Oakland Athletics, New York Yankees and Arizona Diamondbacks. He was a six-time Golden Glove award winner and one-time Silver Slugger award winner.
After retiring at the conclusion of the 2014 season, Chavez became a television analyst before serving in front-office roles for the Yankees and then the Angels.
In August, Chavez became the Triple-A Salt Lake Bees manager after Keith Johnson was promoted to the Angels coaching staff.
Chavez was a special assistant to Angels general manager Billy Eppler before getting his first taste of coaching with the Angels farm club.
Whoever gets the nod as L.A.'s next manager will take over a talented club that is led by perennial MVP candidate Mike Trout.