Moore signed a minor-league contract with the Blue Jays on June 14.
Moore signed a minor-league contract with the Tigers on Saturday.
Moore signed a minor-league contract with the Reds in February.
The Mariners outrighted Moore to Triple-A Tacoma on Sunday.
Moore was optioned to Double-A Arkansas on Wednesday.
Moore allowed four runs in 4.2 innings against Houston on Tuesday but did not factor into the decision. He gave up six hits and one walk while striking out two.
Moore was recalled from Double-A Arkansas to start Tuesday's game against the Astros.
Moore is a candidate to start Tuesday against the Astros in place of Yusei Kikuchi, Ryan Divish of The Seattle Times reports.
Moore was claimed off waivers by the Mariners on Friday.
Moore was designated for assignment by the Giants on Saturday.