Ken Rosenthal of FOX Sports reported on Thursday that free agent pitcher Kyle Lohse and his agent Scott Boras remain in contact with a few major league teams. The Brewers are one of the few teams interested in signing the right-hander, along with the Colorado Rockies and Texas Rangers, according to sources.

From Rosenthal’s post:

“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. “We have too many teams in play,” Boras said.

Lohse, sources say, wants to at least match Ryan Dempster’s two-year, $26.5 million with the Boston Red Sox; the pitcher rejected a one-year, $13.3 million qualifying offer from the St. Louis Cardinals.”

The likelihood of Milwaukee signing Lohse, 34, will be based squarely off general manager Doug Melvin’s willingness to relinquish his club’s 2013 first-round draft pick to the St. Louis Cardinals, which will be the 17th overall selection. However, should Lohse wait to sign with a team until after this summer’s first-year player draft is completed, the Brewers would no longer have to give up that selection.

A week ago, Yahoo! Sports’ Jeff Passan reported via his Twitter page that Lohse’s was seeking a three-year deal valued at $45 million, though those numbers continue to lessen as opening day draws nearer.

Tom Haudricourt of the Milwaukee Journal Sentinel reported on Monday that Brewers manager Ron Roenicke set the club’s starting rotation for the start of the 2013 season. Haudricourt also said that Melvin isn’t expecting to make any moves from now until opening day with respect to the club’s rotation.

Over 33 starts last season, Lohse averaged 6.1 innings per, posting a 2.86 ERA and 1.09 WHIP while garnering a strikeout-to-walk ratio of 3.76, finishing seventh in National League Cy Young award voting. He made a shade under $12 million last season with the Cardinals.

UPDATE: March 24, 1:35 p.m.

Lohse’s asking price per year has been confirmed by ESPN’s Buster Olney at $14-15 million per year.

-AD @alecdopp