DETROIT -- The cutter from Shane Greene was far enough outside for Rangers slugger Joey Gallo, but close enough to the corner to coax a called third strike from plate umpire James Hoye to end the top of the ninth. The remaining crowd at Comerica Park roared, though all the strikeout did was close Texas’ scoring in an eventual 5-3 Tigers loss.

As the fans cheered, the pair of scouts behind home plate jotted down their notes and readied to leave. And so it begins.

While June nears a close, the trading season is just beginning. Tuesday was an early look at Greene, whose scoreless inning lowered his ERA to 0.90 and kept his WHIP at 0.87. Wednesday could bring more evaluators to watch Matthew Boyd’s start as the left-hander tries to rebound from a rough outing last Wednesday in Cleveland against a Rangers lineup that has hit better against righties than lefties. Nicholas Castellanos remains in the background, even as his two-hit game Tuesday raised his average to .303 over his last 31 games and .273 for the season with a .788 OPS, one of the few bright spots in an anemic Tigers offense this month.

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With the Tigers clearly in rebuild mode, general manager Al Avila will listen on all three. But while Boyd could be Detroit’s most valuable commodity for teams to consider, given his upward career trajectory and three more seasons before free agency, Greene could have the widest appeal. Teams can build around a formidable offense or a stingy rotation, but bullpen depth is always a desire for contenders around the July 31 Trade Deadline. Greene, who attracted little to no trade interest over the last two years, is peaking at the right time.

While the Tigers’ summer swoon has dropped Greene down the list of Major League save leaders after he closed 12 wins in March and April, he has remained remarkably useful for a team that sits 22 games under .500 (26-48). He has saved three of Detroit’s four victories in June, and he finished out the other one with a six-run lead. Greene has tossed nine consecutive scoreless innings on five hits since his blown save against the Marlins on May 23.

The metrics show continued value behind Greene’s pitches. While the average exit velocity and hard-hit rate off his pitches are up from last year, he ranks among the top two percent of pitchers in the league in weighted on-base average (wOBA). Greene’s strikeout percentage of just over 25 percent is almost identical to his career high of 2017. Opponents entered Tuesday batting just .132 (5-for-38) off his sinker, compared with .291 a year ago; his cutter has held opponents to .111 (3-for-36), compared to .274 last year.

Greene’s outing Tuesday night wasn’t so much a showcase as it was a refresher, having gone a week since his last appearance thanks to off-days and the Tigers’ current five-game losing streak. He has shown a strong ability to stay effective with all the down time, while serving as a mentor to the many young relievers around him in Detroit’s retinkered bullpen.

While Greene pitches on, the trade market picks up. Multiple executives from clubs viewed as likely sellers at next month’s Trade Deadline told MLB.com’s Jon Morosi that trade inquiries on relievers have picked up in recent days, which could lead to some deals taking place earlier in the month. While the list of buyers might have expanded with the Cardinals losing closer Jordan Hicks to Tommy John surgery, the Indians’ recent resurgence into the American League Wild Card race could take Brad Hand off the market.

Greene has the potential to be one of the most versatile relievers on the market. The converted starter was a multi-inning setup man in Detroit’s bullpen two years ago before Justin Wilson’s trade to the Cubs vaulted Greene into the closer’s job, at which point he began to convert four- and five-out save chances. He has been largely a one-inning closer since Ron Gardenhire’s arrival as the Tigers’ manager, delivering four-out performances just three times last year, but his combination of relative health and efficiency -- he has topped 20 pitches in an inning just five times in 30 appearances this season -- should allow him to shift back into such a role if needed. One National League evaluator who watched Greene last month said he could make an ideal setup man or multi-inning middle reliever for a team with an established closer.

Moreover, Greene still has another season to go before he’s eligible for free agency. Thus, a team on the fringe of contention this year but potentially on the upswing for another run at the playoffs next season could view him as more than a rental option. Greene will be eligible for arbitration one more time this coming winter after making $4 million this season.

That doesn’t mean the Tigers can expect a massive package of prospects in return for Greene. But consider that their highest-ranked hitting prospect (No. 4) by MLB Pipeline, Double-A Erie shortstop Isaac Paredes, arrived from the Cubs in return for Wilson and catcher Alex Avila two years ago at the Trade Deadline, along with third baseman Jeimer Candelario. As Detroit continues to look for impact hitters to add to its system, Greene could give the Tigers another shot.