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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.
Greiss took a third straight loss Wednesday, allowing four goals on 32 shots against the Kings.
Greiss is slated to start Tuesday's game against the Jets, the Coyotes' official site reports.
Greiss made 27-of-29 saves Saturday against Minnesota, but suffered the loss as the Wild scored three unanswered third-period goals to down Phoenix 3-1. The final tally was an empty netter.