Hill is scheduled to make his debut with the Mets on Sunday, Anthony DiComo of MLB.com reports.
The 41-year-old lefty was acquired by New York after posting a 3.87 ERA and 1.16 WHIP in 95.1 innings with the Rays this season. If he does start Sunday, Hill will draw a tough matchup in Toronto's righty-heavy lineup, against whom he allowed three runs in four innings July 11, walking three and striking out two.