On Friday night, former GM Jim Bowden, currently with ESPN, said on Twitter that the Angels were "suddenly the front-runner" to land Oswalt, with the Red Sox still in the hunt and the Rangers and Cardinals fading out.
"I can't qualify for everything you hear," Dipoto said. "But I can say that we're quite happy with the way our starting pitchers have thrown this spring and the way they've developed. You never have enough pitching, so it's tough for me to say that there's not a time in this season where our situation may not change, but right now, we're very happy with where our pitching is."
Jerome Williams, who came into camp as the favorite for the fifth spot, has been out for more than three weeks with a strained left hamstring, but expects to make his first start Monday, which would figure to give him enough time to be ready by April 15 -- the first time the Angels would need a fifth starter.
No. 3 prospect Garrett Richards is also competing for the fifth spot, with Trevor Bell and Brad Mills in camp as other potential options.
Oswalt, 34, had previously said he'd prefer to pitch close to his Mississippi home, but backed off that due to waning interest, telling teams he'd be willing to pitch anywhere and even indicating he's open to a midseason return.
Oswalt's agent, Bob Garber, could not be reached for comment on Saturday.
Dipoto said he's constantly seeking depth behind Jered Weaver, Dan Haren, C.J. Wilson and Ervin Santana, but mostly via Minor League deals or waiver-wire pickups. Like 28-year-old right-hander David Pauley, who was signed Friday but will not report to big league camp.
Pauley, who posted a 3.16 ERA in 53 relief appearances for the Mariners and Tigers last year, will instead get stretched out in the Minor Leagues in hopes of contributing at some point during the season.
"This is an effort to build organizational depth so that when you get to those points in the season, which are inevitable, that you're going to call on pitching depth, and you have guys in Triple-A that provide it," Dipoto said. "David has a chance to be part of that equation."