The actress is said to have "fallen" for the 41-year-old after a mutual friend introduced them in Los Angeles earlier this year.
Stonestreet, who plays Cameron Tucker in the hit US comedy, split from his long-term girlfriend Katherine Tokarz "a couple of months ago".
"Charlize and Eric get along incredibly well. They started off as friends but things are blossoming between them," a source told The Mail On Sunday.
"Eric is down to earth and funny and Charlize thinks the world of him. It's early days but they're very fond of each other."
Theron, who adopted a baby boy named Jackson in March, ended her engagement to Irish actor Stuart Townsend in 2010.