That means signing him would cost the Rockies the 38th overall pick, in Competitive Balance Round A, of the 2016 Draft. The Rockies still would hold three picks in the top 100 -- the No. 4 (first round), No. 45 (second round) and No. 81 (third round) overall selections.
The Rockies' consideration of Gallardo was first reported by MLB Network and SB Nation. Octagon, which represents Gallardo, told MLB.com that the sides planned to meet Thursday. Gallardo has been linked to the Marlins and Blue Jays in recent media reports.
Gallardo, who turns 30 on Feb. 27, went 13-11 with a 3.42 ERA in 33 starts for the Rangers last season. He had spent the previous eight seasons with the Brewers, for whom he went 89-64 with a 3.69 ERA, including an All-Star Game appearance in 2010.
The Rockies have dangled outfielders for much of the offseason in hopes of trading to improve the starting rotation. The signing of outfielder Gerardo Parra to a three-year, $27.5 million contract left the Rockies with four left-handed-hitting outfielders, and left most observers expecting them to trade one -- Carlos Gonzalez, Charlie Blackmon or Corey Dickerson -- for pitching help.
However, by December's Winter Meetings it became clear that dealing an outfielder had the possibility of bringing in either a young Major Leaguer or a prospect.
Such a deal would work with a team that has steadily built a group of young upper-round Draft picks, either with its own selections or acquisitions from other teams. But the current rotation appears to need an established Major Leaguer to work alongside lefty veteran Jorge De La Rosa in setting a standard for less-experienced hurlers.
Gallardo could fit that requirement. After striking out more than a batter per inning from 2009-12, his strikeouts have fallen over the past three seasons, and he recorded only 5.9 whiffs per nine innings in 2015. But many of the other stats have held. Gallardo yielded a career-high 1.42 WHIP last season, his first in the American League. But in 2014, in his final National League season, his 1.29 WHIP was the third lowest of his career.
Thomas Harding is a reporter for MLB.com. Follow him on Twitter @harding_at_mlb, listen to podcasts and like his Facebook page. This story was not subject to the approval of Major League Baseball or its clubs.