PHOENIX – If it were up to the Braves, they will have added more starting pitchers via trade or free agency when the General Managers meetings are completed late Thursday morning.

“It’s a situation where we’ve been aggressive because we’ve got so many starting-pitching needs,” said Braves general manager John Coppolella, who said when the meetings began Monday that adding starting pitchers was priority one, two and three for his team. “We’re trying to push the issue on some key trades or free agents.

“Obviously it takes two to tango, and we don’t have anything yet, but we’re going to continue to search. We’ve made progress on a number of fronts. We’ve still got some work to do. We’ve got some meetings set up (Wednesday) afternoon both with teams as well as with agents, and we hope to continue making progress.”

The Braves made a minor move Monday when they re-signed veteran starter/reliever Josh Collmenter to a one-year, $1.2 million deal. But they’re aiming considerably higher in trying to add a couple of more mid-rotation or better starters.

Word got out Tuesday that the Braves talked to the Tampa Bay Rays about Chris Archer, a 2015 All-Star who has three years left on a club-friendly contract plus two team-option seasons beyond that. Coppolella wondered how that information got leaked when Archer was one of many pitchers they’ve discussed on the free-agent and trade markets since the meetings began Monday.

“We’ve talked to probably 20 teams about starting pitchers, it’s not just the Rays and Chris Archer,” Coppolella said. “I don’t think our conversation with them has been any more or less (involved) than 20 other conversations we’ve had. Does that mean we will or won’t trade for him? No. Chris Archer is really good. I think that any team in baseball will have interest in him.

“He is really good, and the Rays are lucky to have him. But so are a number of other pitchers that may or may not be available in trade. It’s curious to me why that name was leaked but so many others were not.”

Archer turned 28 and had 233 strikeouts in 201 1/3 innings in 2016, albeit with a career-worst 4.02 ERA and 30 home runs allowed. In 2015, the right-hander had a 3.23 ERA with 252 strikeouts in 212 innings.

Given his age, good health and outstanding reputation within both the clubhouse and community, the asking price for Archer is likely to be huge — multiple top prospects or young major league players. That might exceed the comfort level for the Braves, who are reluctant at this stage of their rebuild to trade the most elite prospects they’ve accumulated.

The free-agent class is limited, driving up the price for pitchers who mostly would be viewed as middling if the market was as saturated with arms as it was a year ago. Add to that the Braves’ desire to sign pitchers to contracts of no more than two years and preferably one year, so as not to block the path of the many prospects they have on the way.

Top free-agent pitchers include Jason Hammel, Rich Hill, Ivan Nova, Doug Fister, Bartolo Colon, R.A. Dickey and Edinson Volquez. Jeremy Hellickson could move to the front of that group if he rejects the Phillies’ $17.2 million qualifying offer, but if he does it would cost any team signing him a compensatory draft pick, and the Braves don’t want to give up even a second-round pick (their first-rounder is protected).

“It’s a tough market,” Coppolella said. “It’s a weak starting-pitching market and we’re not the only team that has (similar) needs. Unless it’s a situation where a player really wants to be with the Braves, it may just end up that they need time to do their due diligence, whether it’s a couple of days or a couple of weeks.

“The market just opened and they want do what’s right by their client, many of who have been waiting for this day for a long time.”