Babchuk, 28, is in the final year of his current two-year, $5 million contract and has a salary cap hit of $2.5 million this season.
The native of Kiev, Ukraine, spent time playing for Donbass of the KHL during the locking. He registered one goal, two assists and 22 penalty minutes in 31 games.
If a deal does not immediately present itself, the Sun suggests Babchuk could be used as a rental player closer to the April 3 trade deadline.
In 282 career NHL regular-season games with the Chicago Blackhawks, Carolina Hurricanes and Flames, Babchuk has accumulated 36 goals and 70 assists for 106 points, and 108 penalty minutes.
Babchuk was originally drafted 21st overall by the Blackhawks in the 2002 NHL Entry Draft.