Bauer is scheduled to become a free agent at season's end, and the Reds want to keep the NL Cy Young contender on their squad for the foreseeable future.
"Well, you know, (CEO) Bob (Castellini) and I and (GM) Nick (Krall) and the group will do everything we can to make that happen," president of baseball operations Dick Williams said on Saturday, according to MLB.com's Mark Sheldon.
"I'd love to say yes that there are scenarios where it could happen," he added. "It's honestly not something we're working on today, right now, we're really focused on the postseason, but I'd love to think that Trevor would come back."
Bauer will be one of the most sought-after players if he becomes a free agent. But if he sticks to his word, it's likely the ace will sign a lucrative one-year deal instead of a multi-year pact this offseason.
The 29-year-old said he would "go year-to-year my entire career" in 2019 because of a slowed-down free-agent market. MLB clubs aren't expected to spend lavishly this offseason because of financial issues amid the coronavirus pandemic.
Bauer has authored an exceptional 1.73 ERA, 2.87 FIP, 0.80 WHIP, and 12.3 K/9 pitching line in 11 starts during the shortened regular season.