The 24-year-old forward is set to become a restricted free agent this offseason.
The Chicago Blackhawks general manager Stan Bowman and Andrew Shaw's agent, Pat Brisson, have had preliminary contract discussions, reports Scott Powers of The Athletic.
"I've had some preliminary discussions with Stan," Brisson said by phone Wednesday. "We are talking about it right now. That's pretty much it for now. I have not explored deep enough yet to get a sense [whether we can work something out]. I will have more discussions with Stan in the future.