Milwaukee's offer was first reported Sunday by Yahoo! Japan. Darvish, arguably the best pitcher in this year's free-agent market, retweeted Yahoo! Japan's report later Sunday.
Darvish, who helped the Dodgers reach the World Series last season, is one of several high-profile free agents who remain unsigned with spring training about a month away. The Japanese ace also has been linked to the Rangers, Cubs, Yankees, Twins and Astros this offseason.
A source told ESPN's Jerry Crasnick that Darvish has a five-year offer on the table, although it is unclear whether that offer is from the Brewers or another team. The specifics of Milwaukee's offer to Darvish were not clear as of Monday afternoon.
Houston's interest in Darvish is unclear after the reigning World Series champions acquired starting pitcher Gerrit Cole in a trade earlier this month, but Minnesota is evidently still in the market for the four-time All-Star.
Twins owner Jim Pohlad called himself "a Yu Darvish fan" during an open forum at TwinsFest this past weekend and said he is "totally on board" with Minnesota signing Darvish or another top free-agent pitcher.
Darvish was acquired by the Dodgers from Texas for three prospects just before last year's trade deadline, supposedly the final piece needed to return a championship to baseball's biggest-spending team.
But the 6-foot-5 right-hander only managed four outs in losing Game 7 to the Astros, becoming the second pitcher in World Series history with less than two innings pitched in two starts.
Darvish signed with Texas before the 2012 season and missed all of 2015 after elbow surgery. In 31 combined starts last season, he was 10-12 with a 3.86 ERA.