Markov, who is set to become an unrestricted free agent July 1, is in the final year of a three-year contract worth $5.75 million per season.
It had been widely speculated that the Canadiens might try to move Markov by the March 5 trade deadline if a new contract wasn't reached by then, but multiple sources have told TFP that has never been the case.
TVA Sports is also reporting that a trade is highly unlikely.
According to Renaud Lavoie of TVA Sports, the Canadiens are hoping to sign Markov to a two-year deal, while the 35-year-old blueliner is looking for a three-year deal.
In 59 games with the Habs so far this season, the native of Voskresensk, Russia, has registered five goals and 26 assists for 31 points, along with a plus-7 rating and 26 penalty minutes.