Presumably, any agreement would be pending a physical for Oswalt, who has a history of back problems.
"It's not yet 100 percent," the source said.
On Saturday, Cardinals GM John Mozeliak wrote in an email to ESPN.com's Jerry Crasnick, "These are just rumors, and nothing more."
Oswalt, one of the last big-name free agents still on the market, had been ardently pursued by the Boston Red Sox, among others. Another team reportedly in the mix for Oswalt was the Texas Rangers, while CBSSports.com reported late Friday night that Oswalt had rejected an offer from the Detroit Tigers.
They had targeted Oswalt, 34, once he made it known he would be willing to accept a one-year deal. But Oswalt, who spent the first 9½ seasons of his career with the Houston Astros before going to the Phillies in a trade-deadline deal in 2010, apparently preferred to remain in the National League.
Back problems have plagued Oswalt for the past several seasons, although he still managed to make 23 starts for the Phillies last season, posting a 9-10 record and 3.69 ERA.
Red Sox sources have indicated they expect to re-engage the Chicago White Sox in trade talks for right-hander Gavin Floyd, who, according to one White Sox source, is available for the right package of prospects.
So far, the Red Sox have not made a satisfactory proposal to general manager Kenny Williams.
Edwin Jackson, the last significant starting pitcher remaining on the market, remains a long-shot possibility. Jackson had not been on Boston's radar because of his desire for a multiyear deal, but the Red Sox have been in touch with agent Scott Boras on a possible one-year deal. As of earlier Friday, the Red Sox had not made an offer for Jackson.
They go into camp with three certainties in their rotation: Jon Lester, Josh Beckett and Clay Buchholz. They plan to bring relievers Daniel Bard and Alfredo Aceves to camp with the intention of them becoming starters, and new GM Ben Cherington has signed three experienced starters with injury histories -- Vicente Padilla, Carlos Silva and Aaron Cook -- to minor league deals with an invitation to big league camp.
Manager Bobby Valentine told reporters Thursday that another starting pitcher was not "at the top of my wish list," and the Red Sox might elect to stay put for the time being to see what other options develop between now and the regular-season opener.
Gordon Edes covers the Red Sox for ESPNBoston.com.