The move means the sides can continue to negotiate or go to arbitration. The Red Sox did not tender contracts to infielder Marco Hernández or left-hander Josh Osich, making them free agents.
The Bradley decision was closely watched because the team has said it would like to shed about $30 million in payroll to get under baseball’s luxury tax threshold. To do so, it might now have to trade 2018 AL MVP Mookie Betts.
Bradley batted .225 last season while leading the AL in assists and putouts for a center fielder. He is projected to earn about $10 million next season.