On Saturday, Philadelphia turned down Toronto's first proposal of lefty J.A. Happ, Double-A right-hander Kyle Drabek, its top pitching prospect, and Class A outfielder Dominic Brown, its top position-player prospect.
The Phils countered with a four-for-one package, ESPN.com said, offering Happ and three highly-regarded prospects from Triple-A Lehigh Valley: outfielder Michael Taylor, pitcher Carlos Carrasco and shortstop Jason Donald.
But that was not enough to sway Blue Jays general manager J.P. Ricciardi to part with his ace, the most coveted player in baseball as Friday's non-waiver Trade Deadline approaches. The ESPN.com report said that Toronto will only trade Halladay if it gets "wowed" by an offer.
MLB.com has learned that Jays assistant general manager Tony LaCava scouted Carrasco's latest outing. Toronto seems less eager to accept the 22-year-old right-hander, who allowed six runs in six innings on Friday. Philadelphia, meanwhile, appears willing to trade either Happ (7-1, 2.97 ERA for Phils) or Drabek (10-2, 2.80 at two levels this year), but not both.
The Angels, who are the other team most aggressively pursuing Halladay, are reportedly balking at the Jays' high asking price, ESPN.com said.
Halladay said after his last start that he does not think he will be dealt.
"Right now, yeah, I think I will be here," said Halladay, who is 11-3 with a 2.62 ERA this season. "If there was an urgency to be somewhere else, and an urgency for the team to have me somewhere else, I think it'd be different. I just don't get that feeling."
In case they cannot acquire Halladay, the Phillies have been talking to the Indians about left-hander Cliff Lee, whom they are scouting Sunday. They had previously inquired about Lee, but found Cleveland's asking price too steep at the time.
Philadelphia also has some interest in Pittsburgh left-hander Zach Duke and Seattle left-hander Jarrod Washburn as backup options.
The Jays and Phillies both said that no one was available for comment.
David Gurian-Peck is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.