It isn't yet known what the Brewers would receive in return for Gallardo in the reported deal.
Gallardo, 28, was originally drafted by the Brewers and has remained with the organization during his entire professional career.
Earlier this offseason Milwaukee picked up Gallardo's $13 million team option for 2015. The pitcher will be eligible for free agency after the season.
The Rangers, due in part to injuries to several of the team's starters, ranked 14th in the American League in team ERA last season at 4.49. Texas acquired Ross Detwiler in a trade with the Nationals in December to help bolster its rotation.
Gallardo went 8-11 with a career-best 3.51 ERA in 32 starts for the Brewers last season. In eight major league seasons, Gallardo has gone 89-64 with a 3.69 ERA and a 2.59 K/BB ratio in 214 total games.
The Brewers went 82-80 in 2014 and missed the playoffs for the third consecutive season. The Rangers went 67-95, recording their fewest wins in a full season since 1985, and missed the playoffs for the second straight year.
- Ben Estes