The Red Sox are thin at the position, with newly signed Mike Napoli (who had primarily has been a catcher over his career and comes with hip issues) and Mauro Gomez (15 career major league games started at first) the only first basemen on the roster.
The 36-year-old Overbay would fit well on the Red Sox bench, which is in need of another lefthanded bat and a competent defensive backup at first base.
He has struggled offensively over the past two seasons after hitting 20 homers for the Blue Jays in 2010. Since then, he’s bounced from the Jays to the Diamondbacks to the Braves, performing at a mediocre offensive level at each stop.
His best season came in 2006, when he hit 22 homers and hit .312 for the Blue Jays with an .880 OPS. The Brewers reportedly had also been interested in Overbay.