ESPN The Magazine's Buster Olney earlier reported that the Dodgers had serious interest in bringing in Volquez, whom the Padres designated for assignment Sunday.
The Padres will pay all but the pro-rated minimum of his $5.725 million salary, according to Fox Sports.
Volquez is 9-10 with a 6.01 ERA in 27 starts this season. He has struck out 116 and walked 69 in 142 1/3 innings.
The Dodgers may be interested in Volquez as a possible replacement in the rotation for Chris Capuano, who has a 4.74 ERA in 20 games for the Dodgers this year.