The 27-year-old is making $2 million this season, but should see his salary climb significantly higher on his next contract.
TSN Hockey Insider Bob McKenzie first reported that Emelin and the Habs should be discussing a new deal in the near future.
"Emelin is the guy that's probably first up (among Montreal's pending free agent defensemen) and most likely to get a deal done in the next little while," McKenzie said on TSN.ca. "Nothing's done to this point, but the conversations are headed in that direction and it could get done fairly soon."
Emelin is considered a big, physical force on the blueline and someone the Canadiens count on each game.
Meanwhile, conversations between the Habs and any of their other defensemen in the final year of their respective -- Andrei Markov, P.K. Subban, Francis Bouillon, Raphael Diaz and Douglas Murray -- contracts haven't started.
Subban's agent, Mark Guy of Newport Sports Management, told TFP last week talks haven't gotten underway, though it's believed the Canadiens will soon approach him about a new deal in the coming weeks.