It would be an upset if the Colorado Rockies signed Kyle Lohse. But that hasn’t stopped the Rockies from doing their due diligence on the free-agent right-hander, inquiring about him with different people in the game, major-league sources say.

The Rockies only would sign Lohse “if by a very, very remote chance he just flat-out doesn’t have anything,” according to one source. Even then, the Rockies would need to boost their payroll to get a deal done.

The biggest problem for the Rockies, though, is that Lohse likely would prefer to pitch for a team that plays in a less hitter-friendly environment than Coors Field.

The Texas Rangers and Milwaukee Brewers are maintaining contact with Lohse, sources say. Lohse’s agent, Scott Boras, told MLB Network’s Peter Gammons on Thursday that the pitcher will not wait to sign until after the June draft, when draft-pick compensation no longer would apply.