Lester also met with the Chicago Cubs on Tuesday, according to multiple reports.
Lester, 30, went 6-4 with a 2.35 ERA for the Oakland Athletics after he was acquired in a trade deadline deal with the Boston Red Sox in exchange for outfielder Yoenis Cespedes. Overall, Lester was 16-11 with a career-best 2.46 ERA in 2014.
He started for the A's in the American League wild-card game against the Kansas City Royals and left in the eighth inning with runners on first and second with one out and his team leading 7-4. The Royals won 9-8 in 12 innings.
Lester, who has an offseason home in the Atlanta area, is 6-4 and 2.57 ERA in 14 playoff appearances. He's been dominant in the World Series, where he is 3-0 with a 0.43 ERA in three starts, helping the Red Sox win two championships.
Lester, who has a career mark of 116-67 with a 3.58 ERA in nine seasons, rejected a four-year, $70 million contract extension offer from the Red Sox in the spring. He was paid $13 million last season.