"I don't want to just be a two-month or three-month rental," Victorino said in the report. "I want to be here."
The two-time All-Star was acquired by the Dodgers at the Trade Deadline in exchange for reliever Josh Lindblom and Minor League pitcher Ethan Martin. Victorino is in the last year of a three-year, $22 million contract.
Victorino began his career with the Dodgers after being drafted in the sixth round in 1999. He eventually moved on to Philadelphia, where he developed into one of the game's top outfielders while helping the Phillies win a World Series in 2008.
His numbers have declined this year. He entered Monday's game batting .255 with nine homers, 40 RBIs and 47 runs. He went 2-for-17 in his first four games with the Dodgers.