Milwaukee, famous for acquiring CC Sabathia in July 2008, leads the NL Central by 1½ games.
The Brewers have a top young pitcher in Jimmy Nelson who could interest Boston, and some better prospects than in some recent seasons.
Milwaukee was reported to have interest in Rays star David Price by FoxSports, however Price isn't likely to be traded now that Tampa Bay is back in it. The Brewers might have an easier time competing for a rental such as Lester, anyway.
The Dodgers, Mariners, Pirates and Orioles are among other teams reported to have inquired about Lester.
Milwaukee has been very aggressive in its efforts to win in recent years under owner Mark Attanasio. Sabathia went 11-2 with a 1.65 ERA down the stretch in 2008, leading Milwaukee into the playoffs after he was acquired from Cleveland for outfiield prospect Michael Brantley and slugger Matt LaPorta.