The Phillies would like to have Oswalt or any other starter by this weekend to fill two holes in the current rotation.
But any potential deal can be derailed for various reasons.
Oswalt told reporters in Chicago, where the Astros were playing the Cubs, that he had not yet been asked to waive his no-trade clause in a deal to the Phillies.
"Until they come up to me, there's really nothing I can do," Oswalt said. "I don't want to go up to them and ask them every time something comes across the ticker. So until they come to me, I'll just wait and see."
Oswalt has said he will approve a trade to a contending team. He has made the postseason only twice in a 10-year career spent entirely with the Astros. If presented with the trade, Oswalt would have to decide whether the Phillies have enough to make a playoff run this season.
Manuel said despite his team's offensive struggles, he believes adding another pitcher could be a spark.
"I think the right pitcher could definitely make a difference," Manuel said.
Phillies closer Brad Lidge played with Oswalt for six seasons in Houston. He said he hasn't talked to Oswalt recently but thought he would approve a trade to Philadelphia.
"I've known him for a long time and I saw it day in and day out," Lidge said. "He's a horse out there."
When asked about accepting a trade to the Phillies, Oswalt was noncommittal.
"It would have to work for both of us," Oswalt said. "If it doesn't work for both of us, no. But if it does, maybe."
Ostensibly, he is referring to the prospect of the Phillies guaranteeing his $16 million club option for 2012.
ESPN.com reported that Oswalt would seek that assurance from any other team. The Phillies reportedly have no interest in picking up that option on the 32-year-old.