Markov, 35, is scheduled to become an unrestricted free agent July 1.
Sergei Berezin, Markov's agent, told TFP over the weekend that there was "nothing new" to report, as the two sides continue negotiations.
In 81 games with the Habs this season, Markov registered seven goals and 36 assists for 43 points, along with a plus-12 rating.
The two-time NHL All-Star has played in 765 career NHL regular-season games, all with the Canadiens, and has accumulated 98 goals and 344 assists for 442 points.
Markov was originally drafted by Montreal in the sixth-round (162nd overall) of the 1998 NHL Entry Draft.