Relievers Bob Howry and Chad Fox also filed.
Dempster, who had a career year after converting from closer to starter, has said he would like to remain with the Cubs.
"Absolutely. I love it here," Dempster said two days after the Cubs were swept from the National League Division Series for the second straight season. "I love the city. I love playing here. Hopefully, everything works out."
General manager Jim Hendry shares the feeling.
"Ryan knows we want him to stay here, and he's never expressed a desire that he wants to leave," Hendry said earlier this month. "Certainly, the year he had and type of clubhouse presence he is and total team guy, we certainly have every intention of trying to keep Ryan."
Dempster went 17-6 with a 2.96 ERA in 33 starts, striking out 187. It was perfect timing for a spectacular season, as it came in the final year of a three-year, $15.5 million contract.
Players may only sign with their former club through Nov. 13. If no deal is reached by then, they are free to fully negotiate with other teams. Dempster would certainly get plenty of attention around the league, though the pool of available pitching talent also includes CC Sabathia, Ben Sheets and Derek Lowe.
Edmonds, Howry and Fox, all at least 35 years old, come with more question marks than Dempster. Edmonds was one of Hendry's key additions in 2008. Signed after being released by San Diego in May, the 38-year-old hit .256 with 19 home runs while platooning with Reed Johnson in center. He could retire.
Hendry and manager Lou Piniella have said the team needs more left-handed hitters like Edmonds. However, the Cubs may opt not to pursue him if they would rather let Johnson and 2008 Opening Day center fielder Felix Pie battle for the spot in Spring Training.
In his third year with the Cubs, Howry struggled for all but one month to a 7-5 record and a 5.35 ERA, the highest full-season mark of his 11-year career. Though he was a closer candidate in Spring Training, Howry, 35, quickly fell behind Kerry Wood and Carlos Marmol for late-innings work. The late-season emergence of rookie Jeff Samardzija also overshadowed Howry.
Fox, 38, was never able to fully recover from right elbow troubles that dogged him since 2005. He made three appearances in May, giving up two runs in 3 1/3 innings before hitting the disabled list for the rest of the year.
Closer Kerry Wood, first baseman Daryle Ward, catcher Henry Blanco and right-hander Jon Lieber are the team's other potential free agents.
Nick Zaccardi is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.