The Habs initially offered a one-year extension, but have since upped that to two years, worth around the same $5.75 million, annually, he's earning this season.
It is believed that Markov and his agent, former NHLer Sergei Berezin, are pushing for a three or four year contract.
The Ottawa Senators signed veteran defenseman Chris Phillips to a two-year, $5 million contract extension last week.
Negotiations are expected to continue, though the Canadiens appear firm in their two-year offer.
In 66 games with the Habs so far this season, Markov has generated six goals and 32 assists for 38 points, and a plus-6 rating.