The Braves are out of the Jon Lester sweepstakes, which was a little too rich for the blood of a franchise in transition and rebuilding for 2017 and beyond.

Bidding for the free-agent pitcher already climbed well above $20 million annually in six-year offers from the Cubs, Red Sox and possibly the Giants, and the Braves decided they couldn’t afford a competitive offer for the left-hander, who makes his offseason home in the Atlanta area.

Braves president of baseball operations John Hart and other team officials met with Lester in Atlanta on Nov. 20, and came away as impressed by Lester as a person as they had been by his pitching. Hart said they would’ve loved to have him lead their strong but otherwise youthful rotation. But they wanted to see where the market went before deciding whether to make an offer.

The Cubs offered him $138 million over six years, according to John Heyman of CBS Sports, and the Red Sox, his longtime former team, indicated a willingness to raise an initial offer of $110-$120 million to as high as $130 million. Lester met with the Giants on Monday, and some in the baseball industry believe a bidding war could push the price as high as $150 million.

Lester, who’ll be 31 in January, was 16-11 in 2014 with a 2.46 ERA and 220 strikeouts in 219 2/3 innings. He was 6-4 with a 2.35 ERA in 11 starts for Oakland after a July trade. In the past seven seasons, he won at least 15 games six times, surpassed 200 innings six times, and posted 220 or more strikeouts three times.

Even if Lester had been willing to take less to pitch at his adopted hometown of Atlanta, the Braves didn’t believe they could make an offer near what other suitors were bidding.

The Braves shed about $11 million in projected salaries by trading outfielder Jason Heyward and reliever Jordan Walden to the Cardinals for pitcher Shelby Miller and pitching prospect Tyrell Jenkins, and also lost free-agent pitcher Ervin Santana, who made $14.3 million last season and declined Atlanta’s $15.1 million qualifying offer.

Still, the Braves have about $70 million committed to eight players for 2015, including one no longer on the team. Hart has noted more than $27 million the Braves have tied up for 2015 in a couple of contracts that Hart inherited from fired general manager Frank Wren — $13 million owed Dan Uggla, who was released in July, and $14.45 million for B.J. Upton, part of more than $46 million still owed to the center fielder over the next three seasons.

The team payroll is expected to be similar to last year’s $110-112 million, and the Braves probably won’t have a significant bump higher until they move into a new ballpark in 2017.

The Braves have one vacancy in their rotation and only swing man David Hale, whom they prefer to use in a relief role, as a viable option on the 40-man roster. They have until Tuesday midnight to decide whether to offer contracts to rehabbing arbitration-eligible starters Kris Medlen, who made $5.8 million in 2014, and Brandon Beachy ($1.45 million in 2014), each recovering from a second Tommy John surgery and not expected back before May.