But back problems have robbed him of much of his power and he has batted only .163 since June 2.
Youkilis' salary - he's due $12 million this season, or a little more than $7 million for the rest of the year - had made him difficult to move.
According to Tim Brown of Yahoo Sports, the Red Sox are expected to include $5.5 million in the deal.
With Brent Morel plagued by back problems, the AL Central-leading White Sox have been looking for a third baseman. The Elias Sports Bureau said White Sox third basemen were hitting only .167, making them the worst offensive position in the majors.
The 25-year-old Stewart is 1-2 with a 6.00 ERA in 18 games. Lillibridge, 28, is hitting .175 with two RBIs in 48 games.
The hard-nosed Youkilis played on Boston's World Series champions in 2004 and 2007.
He had two hits on Sunday and received a prolonged ovation after the second, an RBI triple in the seventh. He took off his batting helmet, waved to the crowd, and blew a kiss to his adoring fans.
The Orioles have gone 17 straight games without a stolen base, their longest such streak since a 20-game run in June 1962.
Former Phil succumbs
San Diego bullpen coach Darryl Akerfelds, who played two of his five major-league seasons with the Phillies, died Sunday of pancreatic cancer. He was 50.
Akerfelds had been the Padres' bullpen coach since June 2001. The Denver native pitched for the Phillies in 1990 and 1991, going a combined 7-3. Overall, he appeared in 125 major-league games, going 9-10 with a 5.08 ERA for Oakland, Cleveland, Texas, and the Phillies.
Around the bigs
There has been at least one homer at Minnesota's Great American Ball Park for 62 consecutive games, the longest current streak in the majors. The Twins' Trevor Plouffe and Josh Willingham and the Reds' Joey Votto all connected on Sunday.
Tony LaRussa will become just the second retired manager to lead his league in an All-Star Game. John McGraw retired from the New York Giants after the 1932 season and managed the National League in the first All-Star Game the following year.
On Monday night in Colorado, Washington righthander Stephen Strasburg can become the first player in Nationals history to win seven consecutive starts.
Elsewhere: Boston's Clay Buchholz was placed on the 15-day disabled list Sunday with what manager Bobby Valentine called a "gastrointestinal issue." . . . The Padres placed righthander Anthony Bass (right shoulder inflammation) on the 15-day DL.
Contact Don McKee at firstname.lastname@example.org.
This article contains information from the Associated Press.