Samardzija, 30, spent his first six-plus Major League seasons with the Cubs after being drafted by Chicago in the fifth round of the 2006 Draft. He was traded to the A's midway through the 2014 season, then returned to the Windy City via a trade to the White Sox in December 2014.
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Last year with the White Sox, he went 11-13 with a 4.96 ERA. Over his eight-year career, Samardzija is 47-61 with a 4.09 ERA.
Epstein has said the Cubs are pursuing multiple starting pitchers even though they have Cy Young winner Jake Arrieta, Jon Lester, Kyle Hendricks and Jason Hammel under team control. They would lose a Draft pick (since Samardzija turned down a $15.8 million qualifying offer from the White Sox) if Samardzija signs with the Cubs, but if the team loses center fielder Dexter Fowler (who turned down the Cubs' qualifying offer) to another team, they'll gain a pick that way.
Samardzija has strong ties to Cubs pitching coach Chris Bosio, and the team has continued to keep a close eye on the right-hander, particularly after he returned to Chicago last year.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.