Wagner’s agent, Bean Stringfellow, has indicated that the pitcher might be open to accepting arbitration and remaining with the Sox, even though they would keep using him as a set-up man instead of a closer. Wagner was at the end of a four-year, $43 million deal, and the Sox declined his $8 million option. General manager Theo Epstein has said that the Sox would be happy to have Wagner back.

Because the Sox have offered arbitration, they will receive draft picks in compensation if Bay and Wagner, both Type A free agents, sign elsewhere.

But it was not only their own free agents the Sox were interested in yesterday. They also had their eye on Marco Scutaro, a potential shortstop replacement for the Sox, who was offered arbitration by the Blue Jays. That makes him, another Type A free agent, a bit less attractive to Boston.

To that end, and with the Blue Jays already having scooped up Alex Gonzalez, the Sox checked in with their second baseman, Dustin Pedroia, about the possibility of taking over a different position.

According to a report by Peter Gammons on ESPN.com, Pedroia responded positively to the suggestion of playing shortstop. Pedroia played the position at Arizona State and in the minors.

Efforts by the Globe to reach Pedroia were unsuccessful, but he told Gammons, “They’ve asked me if I think I could play shortstop. They’ve put it out there and I’ve told them I’m all for it. I can do it. I can’t wait for Tito [Terry Francona] to call me and ask, ‘Can you do it?’ I can do it. I really want to.’’

A team source said that while the issue has been raised within the organization, it would not happen unless the Sox absolutely cannot find another shortstop. While it is an intriguing idea for some in the organization, there are far more palatable options for the time being.

The Sox did not offer arbitration to Rocco Baldelli, Paul Byrd, and Chris Woodward.

Nick Cafardo of the Globe staff contributed to this report.