The extension is expected to be for three or more years and worth $9 million or more annually, a person familiar with the situation told the newspaper.
A new deal would more than likely replace a $12 million option the Braves have on Hudson's contract for 2010, the Journal-Constitution reported. The club has until three days after the World Series to pick up the option.
The 34-year-old right-hander went 2-1 with a 3.61 ERA in seven late starts for the Braves in 2009 after a yearlong recovery from Tommy John surgery. The former 20-game winner has a 148-78 career record with the Braves and Oakland Athletics.