Rockies general manager Dan O'Dowd, however, remains resistant to paying "full price'' for Rodriguez, the source said. Rodriguez is owed $37 million from 2012 through 2014.
The talks were first reported by the Houston Chronicle and FoxSports.com.
Rodriguez, a lefty, is 9-9 with a 3.31 ERA.
The Astros have 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, scheduled to pitch Wednesday against Colorado in his 200th career appearance, responded to the Chronicle.
"It's hard, because I don't know what's going on," Rodriguez said. "And I pitch (Wednesday). Will they trade me, or do I stay here? Will they make a decision today or tomorrow? Maybe tonight, because I'm pitching tomorrow?"
The Rockies also activated right-hander Alex White from the 60-day disabled list to start against the Astros on Tuesday night.
White, one of four players acquired from Cleveland in the trade
that sent Ubaldo Jimenez to the Indians last month, struggled in
his Colorado debut. He allowed five runs on seven hits and struck out
four in six innings in a 8-6 win in Denver.
To make room for White on the 40-man roster, the Rockies transferred right-hander Juan Nicasio to the 60-day DL.
Information from ESPN.com's Jerry Crasnick, ESPNNewYork.com and The Associated Press was used in this report.