The Canadiens assigned Dubnyk to Hamilton of the AHL shortly after the trade.
Price told reporters Tuesday that he was making progress in his return from a lower-body injury suffered at the Sochi Olympics but acknowledged that there is no timetable for his return.
Budaj is expected to make his fifth consecutive start Wednesday against the Anaheim Ducks.
Dubnyk, who already was traded this season from the Edmonton Oilers to Nashville, had been placed on waivers earlier this week by the Predators.
A five-year veteran, Dubnyk is 11-18-3 in a 34 games this season with Edmonton and Nashville.