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Eight teams have reached out to Greiss' agent, reports Sarah McLellan of the Arizona Republic. He becomes a free agent on July 1.
Greiss allowed just two goals on 23 shots Thursday against the Preds, but the Coyotes scored none to support him.
Greiss is expected to start Thursday's game against the Predators, the Coyotes' official site reports.
Greiss stopped 24 of 26 shots but allowed the only goal of the overtime shootout and lost to the Oilers' 3-2 on Friday.