The Red Sox's most recent offer to Lester was far below market value -- four years for between $70 million and $80 million, according to sources within the team's clubhouse.
Lester, who is eligible for free agency at the end of the season, rejected the offer and will not resume negotiations with the club until the offseason, the sources said.
The Red Sox will have an exclusive negotiating period with Lester between the end of the season and the start of free agency. They indicated a willingness to go higher, sources said, but are almost certain to lose Lester unless they dramatically increase their offer.
Lester has expressed a willingness to give the Red Sox a hometown discount. But the team's offer is not in line with recent activity on the starting-pitching market.