A deal is not close, and the Padres are "exploring multiple options," according to Rosenthal.
The Dodgers outfielder signed an eight-year, $160 million contract with Los Angeles in 2011, which runs through the 2019 season.
Kemp hit .287 with 25 home runs, 89 RBI and a .346 on-base percentage in 150 games in 2014. In four postseason games, he hit .353 with a home run and two RBI.
The 30-year-old started last season in center field before being moved to left by manager Don Mattingly in May because Kemp was struggling defensively. He later moved to right field, where he had not played regularly since 2009.
Kemp has spent his entire nine-year career with the Dodgers. The outfielder has a career .292 average with 182 home runs and 648 RBI. He was named an All-Star in 2011 and 2012 and led the National League in home runs in 2011 with 39.
- Molly Geary