But much to the Phillies' chagrin, two people who know Oswalt well said he prefers to pitch in St. Louis.
Sources who have spoken with the Astros say that while St. Louis might be Oswalt's first choice, trading their best pitcher within the division isn't the team's first choice. The Astros continued to talk to the Phillies and also have tried to lure other clubs into the bidding.
A source told ESPN.com that Astros owner Drayton McLane was likely entertaining the trade talks as a favor to Oswalt, a franchise cornerstone, but if Oswalt pushed too hard, he could overplay his hand.
Clubs the Astros have spoken with say Houston is looking for four players in return -- one player who is either on the major league roster or is major league ready; two "high-end" prospects; and one second-tier prospect.
According to a source familiar with the teams' conversations, the Cardinals indicated to Houston they would make outfielder Jon Jay and infielder Brendan Ryan available from the current roster. And, among the prospects the Astros are likely to press for is last year's No. 1 pick, 19-year-old right-hander Shelby Miller.
The Phillies, meanwhile, are thought to have offered pitcher J.A. Happ and a list of younger prospects for the Astros to choose from. But Houston is looking for higher-ceiling young players, particularly a catcher and/or corner infielders, than the names on that list.
Other clubs report the Phillies have continued to shop outfielder Jayson Werth in the last 24 hours, in part to see if he could bring back a prospect or prospects that would help them complete the Oswalt trade. But there were no signs they were making headway with any team on Werth.
Oswalt is asking the Phillies, or any team that acquires him, to guarantee his $16 million option in 2012 before he would approve a trade, according to two sources familiar with the discussions.
On Friday, a source told ESPN.com's Amy K. Nelson that Oswalt would not budge from that demand.
Though he is unlikely to forgo the option, the source told Nelson that Oswalt has indicated to the Astros that he would be willing to restructure his deal for the Cardinals. The Phillies and other interested clubs have balked at picking up the pitcher's option.
"In the end," an official of one AL team said, "I don't believe the guy is going to insist on getting that option picked up. He wants out. And if he really wants out, that's going to change."
Oswalt, 32, has about $7 million left on his $15 million salary for this year, plus a guaranteed $16 million next season and either a $2 million buyout or that $16 million option for 2012.
Oswalt's agent, Bob Garber, has not returned multiple calls from ESPN.com in the last 48 hours.
Jayson Stark is a senior baseball writer for ESPN.com. ESPN the Magazine's Buster Olney and ESPN.com's Jerry Crasnick also contributed to this report.