The Senators have been looking to trade the 28-year-old netminder and Friedman reported Thursday that Ottawa held conversations with Buffalo, however, the Sabres are on Murray's no-trade list and he stuck to it.
Murray has two more years left on his current deal that has a $6.25 million cap hit.
He posted a 5-12-2 record with a 3.05 goals-against average and a .906 save percentage this past season and dealt with injuries including a concussion that kept him out of the lineup for the final 28 games of the campaign.
Ottawa recently re-signed Anton Forsberg to a three-year extension and also has Filip Gustavsson under contract until 2023.
Toronto traded goalie Petr Mrazek to the Chicago Blackhawks during the NHL Draft while starter Jack Campbell is slated to become an unrestricted free agent on July 13.