The 27-year-old from Dearborn, Mich. faced 40 shots in a 3-2 loss to the New Jersey Devils on Tuesday night.
He has been recalled by many teams, including the Predators, Blue Jackets, Bruins and the Avalanche this season, but has yet to see any game action.
A deal does not appear likely however, as the price of the pieces the Senators would want (presumably either Matt Duchene or Gabriel Landeskog) is too high.
It's a rumor that just will not go away. The Boston Bruins and the Colorado Avalanche remain connected on the trade front.
On Sunday Colorado was outscored 5-1 by the Islanders in Brooklyn, allowing three goals in the third period for the second straight night.
Henrik Lundqvist earned his 400th career win, making 32 saves, as the New York Rangers defeated the Colorado Avalanche at Madison Square Garden on Saturday.
"Possibly Varlamov too, [who] you can get for, oh, a bucket of pucks," Frei told Kent Eriksson, Irv Brown and Joe Williams on Mile High Sports Radio.
After placing him on waivers for the second time this season, the Colorado Avalanche have assigned defenseman Eric Gelinas to the AHL's San Antonio Rampage.
Colorado, winners of their previous two, has yet to string together three consecutive wins this season and fell to 15-34-2 with the loss.
Colorado Avalanche goaltender Calvin Pickard will have a new backup when the team faces the defending Stanley Cup champion Pittsburgh Penguins on Thursday.