Stuart, 26, has a goal and four assists with a plus-8 rating and would fill a role that Blackhawks general manager Stan Bowman recently said they needed to upgrade.
"We're trying to find a defenseman that can be a penalty-killing type," Bowman said last Friday. "Right now, we're using our top guys a lot.
"In a perfect world we could get a guy to come in and do that."
Stuart has a salary cap figure of $1.675 million, and it's believed the Blackhawks would have to alleviate some payroll before adding him.
CSNNE.com first reported that the Bruins are discussing sending Stuart to the Blackhawks.
The NHL trade deadline is Feb. 28.
Jesse Rogers covers the Blackhawks for ESPNChicago.com and ESPN 1000.