Watch Now: Scott Boras: Dallas Keuchel will be ready to pitch in a week once signed (1:07)

As the 2019 MLB Draft nears, the Dallas Keuchel rumors are starting to heating up. Keuchel, still unsigned as we enter June, will no longer be attached to draft-pick compensation once the first day of the draft comes, approximately at 12:01 a.m. ET on Monday, June 3.

As that deadline approaches, Keuchel has lowered his contract demands and is now open to a one-year deal. One of the bigger questions and concerns for teams interested in signing the veteran lefty is how quickly will he be ready to pitch at the MLB level after spending more than a third of the season as a free agent.

Scott Boras, who represents Keuchel, told MLB Network's Jon Morosi that he believes the southpaw will be ready to pitch in MLB games within roughly one week after signing. Boras also added that Keuchel has thrown seven simulated games (95-104 pitches), every five days, to prepare for an eventual starting role with a team.

Keuchel, 31, didn't join a team in spring training, and he hasn't pitched in a major-league game since last October. It's hard to take what Boras said seriously. It's not farfetched to imagine that Boras is just doing his job and publicly talking up his client so he can sign a deal soon. The concern of Keuchel being a little rusty is a reasonable one, and I doubt any team that locks him up will want to throw him into the fire a week after signing. Keuchel will probably need a quick minor-league stint so he can get some experience pitching in real games before joining a big-league rotation.

The Yankees, Rays, Twins, Braves, Cardinals and Brewers were MLB teams recently connected to having interest in Keuchel.

The 2015 American League Cy Young winner posted a 3.74 ERA and a 1.31 WHIP in 204.2 innings last season. Free-agent closer Craig Kimbrel could also sign with a team and pitch the final two-thirds of the 2019 season. It's expected that negotiations with both free agents won't gain serious momentum until the draft deadline passes and clubs won't have to surrender draft compensation to sign either.