Per ESPN's Jeff Passan, the Dodgers are "monitoring" the market for Bauer and could get involved in talks with him if his price lines up with what they are willing to spend.
Bauer is the biggest free-agent domino still standing, with no indication that he will be arriving at a decision any time soon.
The 2018 All-Star said in a video post last month that he had a meeting with the Toronto Blue Jays. It's unclear if Toronto will invest another large contract in free agency after MLB Network's Jon Heyman reported on Tuesday it agreed to a six-year, $150 million deal with George Springer.
Heyman noted the Dodgers are also looking at right-handed hitting infielders, with Justin Turner at the top of their wish list.
Turner, Joc Pederson and Enrique Hernandez are the three key players from Los Angeles' World Series team last season who are still free agents.
Heyman reported last month that Bauer is seeking a five- or six-year deal worth between $36-40 million per season.
Bauer, 30, is coming off the best season of his career. He led the NL with a 1.73 ERA and had 100 strikeouts in 73.1 innings over 11 starts for the Cincinnati Reds.
The San Diego Padres have made bold, aggressive moves for Yu Darvish, Blake Snell and Joe Musgrove this offseason. The Dodgers aren't starved for starting pitching with Walker Bueler, Clayton Kershaw, Dustin May and Julio Urias, but they can't afford to rest on their laurels with the Padres on their heels in the NL West.