While waiting for Lee's decision, the Dodgers pulled out of the proposed trade earlier, sources told Olney.
Lee has a limited no-trade clause and his permission was needed to complete the deal.
One baseball official familiar with the discussions told ESPN.com's Jayson Stark that the Dodgers and Astros agreed on the framework of the trade before presenting it to Lee for approval. Although rumors have circulated about a 2-for-1 deal, the Astros would have received just one minor leaguer from the Dodgers. One name in play was right-handed pitching prospect Garrett Gould, who abruptly was scratched from his start Friday for Class A Rancho Cucamonga.
The official also told Stark the Dodgers would pay a significant chunk of the more than $8 million remaining on Lee's salary.
Lee, 36, is in the final year of a six-year, $100 million contract.
The injury-depleted Dodgers, missing Matt Kemp, Andre Ethier and Mark Ellis, were shut out for the sixth time in 12 games on Saturday against the Mets and have produced only two runs in their last 57 innings. They are in a 1-11 tailspin that has seen them go from five games ahead in the NL West to a 1½ behind surging San Francisco. Los Angeles led by 7½ games on May 27.
Information from The Associated Press was used in this report.