No financial terms were disclosed in the report. According to Nick Cafardo of The Boston Globe, the Red Sox have also made an offer to third baseman Pablo Sandoval.
Lester, 30, turned down a four-year, $70 million offer made by Boston in March and was subsequently shipped to the Oakland Athletics on July 31 for outfielder Yoenis Cespedes. He could command as much as $150 million with his next contract; he made $13 million last season.
The pitcher is expected to take his time making his decision, according to ESPN's report.
Sandoval met with the Red Sox in Boston this week and has said he wants a six-year contract in free agency. The Red Sox are reportedly "all-in" to sign Sandoval, who could reportedly land a contract worth $90 million to $100 million on the open market.
Lester went 16-11 with a 2.46 ERA with 220 strikeouts last season for Boston and Oakland. In eight MLB seasons, Lester has compiled a 116-67 record with a 3.58 ERA with 1,457 strikeouts.
A two-time All-Star, Sandoval won three World Series with the Giants, including in 2014 when he batted .279 with 16 home runs and 73 RBIs.
- Scooby Axson and Molly Geary