It was not known who the Padres would receive in return for the 42-year-old right-hander, the newspaper said.
Dodgers spokesman Josh Rawitch and General Manager Ned Colletti told the Times no deal was in place and declined to say whether discussions in a deal were under way.
Maddux, who had a career-long 14-start winless streak earlier this season, pitched for the Dodgers at the end of the 2006 campaign after being acquired from the Chicago Cubs. He signed with San Diego prior to the following season.
This year, Maddux is 6-9 with a 3.99 earned run average, but has given up just four runs over 19 total innings in his past three starts. Maddux was 14-11 with a 4.14 ERA in his first season with San Diego in 2007.
For his career, Maddux has a record of 353-222 with an ERA of 3.14. His win total is ninth all-time, one behind Roger Clemens.