According to the TEAM 990 radio in Montreal, Markov approached the goaltender after the 4-3 loss in overtime and told him "If you are not going to play with heart, stay home. We don't need you here."
The radio station's account also stated the dressing room was split with some players coming to Price's defence and others siding with Markov.
The Canadiens had no comment on the report.
Price is expected to get the start against the Tampa Bay Lightning on Wednesday night. The 22-year-old has a 11-16-4 record with a 2.73 GAA and .913 save percentage this season.