The free-agent pitcher has plans to meet with the World Series champions on Monday, a source told ESPN's Buster Olney.
San Francisco has need for a front-line starting pitcher and was expected to get busy in the free-agent market after losing the slugging third baseman to the Boston Red Sox. Lester would join World Series MVP Madison Bumgarner to give the Giants two top left-handers at the top of their rotation.
Lester, who turns 31 in January, was dealt by the Red Sox to the Oakland Athletics at the trade deadline in July and helped the A's reach the playoffs for the third straight year before a 9-8, 12-inning loss to Kansas City in the AL wild-card game.
Oakland general manager Billy Beane said after the season he didn't think his club would have made it that far without the addition of Lester, who was 6-4 with a 2.35 ERA in 11 starts and 76 2/3 innings with the A's. He was 16-11 overall with a 2.46 ERA in 32 starts and a career-high 219 2/3 innings.
Giants right-hander Matt Cain is recovering from elbow surgery that ended his season in July and right-hander Ryan Vogelsong is a free agent. Manager Bruce Bochy has said two-time NL Cy Young Award winner Tim Lincecum, who played a minimal role this past postseason, will begin the 2015 season in the rotation. Tim Hudson, a 39-year-old righty signed through '15, rounds out the current starting staff.
ESPN's Jim Bowden and The Associated Press contributed to this report.