According to an industry source, the Red Sox have checked in on right-hander Ryan Dempster. The 35-year-old was 12-8 with a 3.38 ERA in 173 innings in 2012 with the Cubs and Rangers, though he went 7-3 with a 5.09 ERA after Texas acquired him at the trade deadline.

Though 35, Dempster has been durable with a strong track record since moving from the bullpen to the rotation with the Cubs in 2008. Over the last five years, he’s averaged 199 innings a year (2012, in fact, was the first time in that span during which he’d failed to log 200 innings) with a 65-49 record and 3.74 ERA.

The right-hander, according to a source familiar with his thinking, is seeking a three-year deal. With Dan Haren having agreed to a one-year, $13 million deal with the Nationals (pending a physical), Dempster will likely use that figure as a baseline for the average annual value he seeks.

Dempster vetoed a potential deal to the Braves last summer, when he preferred to go to the Dodgers at the trade deadline, but ultimately, when Los Angeles didn’t part with prospect Allen Webster (who later was traded by the Dodgers to the Sox in the August blockbuster), Chicago dealt him to Texas for minor league third baseman Carlos Villanueva.

Dempster is not ruling out any teams on the basis of geography. While the longtime NL pitcher (he’s spent all but two months of his career in the National League) has a slight preference to stay in the senior circuit, he isn’t ruling out teams on the basis of that.

Dempster figures to be among the pitchers whose market will heat up after the top tier free agent starters (Zach Greinke, Anibal Sanchez) find new landing spots.