Mets manager Luis Rojas said Hill would arrive at the ballpark before Saturday night's game against the Blue Jays and throw on the side.
The Mets acquired the 41-year-old left-hander in a trade with the Tampa Bay Rays on Friday for veteran pitcher Tommy Hunter and minor league catcher Matthew Dyer.
Hill went 6-4 with a 3.87 ERA in 19 starts for the Rays this season. He faced Toronto on July 11 and gave up three runs on four hits and three walks in five innings.
Hill will be a much-needed addition to a starting rotation that has been depleted by injuries, most notably ace Jacob deGrom being on the 10-day injured list with tightness in his right forearm.
Left-hander David Peterson had been expected to return sometime in August after being sidelined with an oblique strain, but the Mets announced Saturday they were moving him to the 60-day IL after he fractured his right foot walking back to the clubhouse following Friday night's win.
Rojas also said righty Carlos Carrasco will make a rehab start with Triple-A Syracuse on Sunday.
Carrasco hasn't pitched in the majors this year while recovering from a hamstring injury. He's started twice in the minors, allowing five runs in 3⅔ innings.