Reports on Tuesday suggest the Philadelphia Phillies, Houston Astros, and New York Yankees have also emerged as potential suitors for the 27-year-old.
Ray, a former All-Star, could provide a solid boost to a Brewers rotation that has underwhelmed this season. The team's starters have accrued a collective 4.73 ERA, which is good for 18th in the majors.
The emergence of Brandon Woodruff and Zach Davies has been a positive development for Milwaukee. However, the club needs more production from the rest of the rotation - including last year's de facto ace Jhoulys Chacin (5.18 ERA) - if it hopes to contend in a tight National League Central. The Brewers (48-47) sit 2 1/2 games behind the Chicago Cubs for the division lead but only three games clear of last place heading into Tuesday's action.
Ray, who's under team control through 2020, has pitched well in 111 innings this campaign for Arizona. He's notched the second-most strikeouts in the NL (145) while putting up a 3.81 ERA across 20 starts.
The Diamondbacks (47-47) are in second in the NL West but sit 15 games back of the Los Angeles Dodgers. However, Arizona is just one game out of a wild-card spot so it remains unclear if the team will be a buyer or seller ahead of the July 31 trade deadline.