The Angels hosted Konerko in Anaheim on Monday afternoon and for most of Tuesday for meetings that Stoneman said were very positive.
"I know we were very attractive to him," Stoneman said. "But I also know it would be tough to leave a World Series champion."
Konerko was a part of the first World Series title in Chicago since 1917. The first baseman also won MVP honors in the American League Championship Series by hitting .286 with two homers and seven RBIs as the White Sox eliminated the Angels.
The Angels hit .175 in that series and have looked this offseason to find a bat to place in the middle of the order to add power and help Garret Anderson protect Vladimir Guerrero.
Konerko had cited playing on the West Coast and being near his offseason home of Scottsdale, Ariz., during Spring Training, two things the Angels could offer, as two key factors in deciding his future. But his South Side roots had planted further than he anticipated.
"It's as simple as where your heart is," said Konerko, who hit 40 homers last season and drove in 100 runs. "That's what brought me back."
All of which puts the Angels back in search of a hitter to strengthen the offense for 2006.
Red Sox outfielder Manny Ramirez has been mentioned in numerous trade rumors, but the free-agent class also includes outfielders Johnny Damon, Brian Giles, Jacque Jones, Reggie Sanders, Rondell White and Preston Wilson.
Catcher Mike Piazza is also available, but he is 37, and none in the group compares from a power perspective with Konerko, whose 81 homers over the past two years are fourth in the AL behind David Ortiz, Ramirez and Alex Rodriguez. Ramirez has hit 88 homers and driven in 274 runs over the last two seasons.
Stoneman said Konerko is simply one less candidate to consider, but he would not elaborate on which direction the club would take next, whether it is the free-agent or trade route.
"We're going to continue to pursue different free agents and talk to other clubs and how that sets up how we handle the guys on our own club," Stoneman said. "When you look at it at the end of the day, we're still a very good ballclub. The only time you want to change that is if you make yourself a better ballclub."
A key free agent of the Angels is Paul Byrd, who has been fielding offers from at least three other clubs. The Orioles, Rangers and Indians are all reported to be interested, which has prompted the Angels to consider increasing their one-year offer to the right-hander. Byrd went 12-11 with a 3.74 ERA in 31 starts for the Angels last season.
Not signing Konerko could also produce dividends for some of the young prospects in the organization.
First baseman Casey Kotchman, whom Stoneman described as having "a really good future," would likely have seen his advancement blocked, but Wednesday's development also opens the door for players such as Kendry Morales and Brandon Wood to make a mark this spring.
"We have some players that are very close to being with the Angels," Stoneman said.