Now that the offseason has begun, we’re likely in for several weeks of rumors centering on longtime Giants left-hander and current free agent Madison Bumgarner. Let’s get the ball rolling in earnest: Atlanta has “made Bumgarner a priority and planned to quickly communicate that to the left-hander,” Alex Pavlovic of NBC Sports California reports. If Bumgarner doesn’t re-sign with the Giants, the Braves are the front-runners for his services, according to Pavlovic.

For now, Bumgarner has until Nov. 14 to decide whether to accept the $17.8MM qualifying offer the Giants gave him earlier this week. But rejecting it looks like a formality for the 30-year-old Bumgarner, who MLBTR projects will land a four-year, $72MM contract on the open market. Whether the numbers are exact remains to be seen, but Bumgarner’s surely in line for a substantial payday, so the main question is whether San Francisco will be the team that hands it to him.

The Giants are the lone club Bumgarner has known since they selected him 10th overall in the 2007 draft. Although he has since turned into a decorated hurler who has helped the Giants to three championships, there hasn’t been any indication that the team has seriously pursued a contract extension. The Giants did elect against selling off Bumgarner prior to the July 31 trade deadline, but it’s possible they would have gone another way had it not been for an improbable midsummer surge. The team ultimately faded after its torrid July stretch, finishing 77-85, and now it could lose Bumgarner for nothing more than draft-pick compensation if he rejects its QO and heads elsewhere.

In the event Bumgarner does leave the Giants, Atlanta looks like a reasonable fit on paper for the North Carolina native. With Dallas Keuchel now on the free-agent market, the Braves are known to be looking for at least one capable veteran starter to complement Mike Soroka, Max Fried and Mike Foltynewicz. And Bumgarner, unlike Gerrit Cole or Stephen Strasburg (the top two starters available), wouldn’t cost a bank-breaking amount or force the Braves to make an extraordinarily long-term commitment. Of course, there’s an obvious reason for that: Bumgarner, despite his past accomplishments, isn’t nearly as good as Cole or Strasburg at this point. While he was a front-line starter during his younger days, Bumgarner now looks more like a quality mid-rotation arm.

Bumgarner’s on the market fresh off a 207 2/3-inning season (his seventh year of 200-plus frames) in which he pitched to a matching 3.90 ERA/FIP with 8.8 K/9, 1.86 BB/9 and a career-low 35.8 percent groundball rate. For the most part, those numbers look closer to good than spectacular, though they’d still be welcome in just about anyone’s rotation – including the Braves’.

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