Verrett was selected in the Rule 5 draft in December by the Baltimore Orioles. He was claimed off waivers by the Texas Rangers on the eve of the season and made the team's Opening Day roster as a reliever.
Verrett, 24, allowed seven runs (six earned) on 11 hits and four walks in nine innings with the Rangers out of the bullpen.
He was designated for assignment on Friday, with the Rangers needing a roster spot for Wandy Rodriguez.
Texas can look to trade Verrett during the DFA process, with the Rule 5 stipulations applying if a team acquires him. If Verrett goes untraded, he ultimately will need to go through waivers. Assuming he clears waivers, Verrett then would be offered back to the Mets.
Verrett went 11-5 with a 4.33 ERA in 28 starts for Triple-A Las Vegas last season.