Rockies general manager Dan O'Dowd was resistant to paying "full price'' for Rodriguez, a baseball source told ESPN.com's Jerry Crasnick. Rodriguez is owed $37 million from 2012 through 2014.
The move came after Rodriguez allowed six runs, four earned, in six innings in a 10-inning loss to Colorado on Wednesday.
Rodriguez said the uncertainty didn't bother him Wednesday.
"I thought about it a lot (Tuesday) night," he said. "I didn't know if I would be pitching here or over there."
The Astros had until 1 p.m. ET Thursday to complete a trade for the 32-year-old pitcher or pull him back off waivers and keep him.
Rodriguez, a lefty, is 9-9 with a 3.41 ERA in 24 starts this season.
Information from The Associated Press contributed to this report.