Lee told MLB.com that he has been informed by Astros general manager Jeff Luhnow that trade discussions with the Dodgers have included the first baseman. Since he has a limited no-trade clause, Lee would have to approve the deal.
Lee has told the Astros, though, that he doesn't want to waive the no-trade clause, a source told ESPN The Magazine's Buster Olney.
When Lee arrived at Wrigley Field for a game against the Cubs on Saturday, he said, according to MLB.com: "I met with Jeff this morning and he told me what's going on and let's see what happens."
"I just told Jeff I want to see my options. I just want to wait and see what my options are," Lee added.
Dodgers manager Don Mattingly said he'd heard the rumors about the his team pursuing Lee, but did not know the status of the talks.
The Dodgers believe Lee is "still thinking about it," a source told ESPNLosAngeles.com.
When asked if he could understand a player deciding not to waive a no-trade clause despite an opportunity to play for a contender -- as Dodgers starter Hiroki Kuroda did last season -- Mattingly said:
"Yeah, if a guy's comfortable where he's at and he doesn't want to leave home, he's got kids and a family and he says, 'You know what, I don't want to go out there...
"If the guy doesn't want to take a shot at winning and getting to the playoffs, maybe winning a World Series, if he doesn't want that, then we probably don't ... "
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 receive just one minor leaguer from the Dodgers. One name in play is 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 is in the final year of a six-year, $100 million contract. He said he was not given a deadline to decide.
The 36-year-old is batting .290 with five homers and 29 RBIs this season.
Lee has deep roots in Houston and was asked if he would like to join a contender.
"That's one of the things I have to think about," he said, according to MLB.com. "There ain't much I can tell you right now."
The injury-depleted Dodgers, missing Matt Kemp, Andre Ethier and Mark Ellis, were shut out for the fifth time in 11 games -- including all three at San Francisco -- on Friday against the Mets and have produced only two runs in their last 48 innings. They are in a 1-10 tailspin that has seen them go from five games ahead in the NL West to a game behind surging San Francisco. Los Angeles led by 7 1/2 games on May 27.
Information from ESPNLosAngeles.com's Ramona Shelburne and The Associated Press was used in this report.