TODAY, 3:27pm: The Mariners and Rangers are also out on Kemp, Heyman tweets.

2:20pm: The Orioles are out on Kemp, sources tell Eduardo Encina of the Baltimore Sun. Baltimore had concerns with Kemp’s long-term health and talks went nowhere after the Dodgers asked about young pitchers Kevin Gausman and Dylan Bundy.

1:20pm: Another name that has come up is 20-year-old righty Zach Eflin, according to Jon Heyman of CBSSports.com.

Wisler is not going to be included in any deal, Rosenthal now tweets, though righty Joe Ross could be.

12:05pm: The sides are still working hard on a deal and have made progress, tweets Rosenthal. Los Angeles is looking for another quality piece in addition to Grandal, with strong pitching prospect Matt Wisler being a “possibility,” per Rosenthal.

YESTERDAY, 10:53am: The talks have run “hot and cold,” a source tells Ken Rosenthal of FOX Sports. San Diego does have focused interest in Kemp, though Justin Upton could be an option as well. (Twitter links.)

10:27am: The Padres are the team that is most likely to land Dodgers outfielder Matt Kemp via trade, according to Bob Nightengale of USA Today (via Twitter). Recent reports had tied the two clubs in talks.

San Diego’s current offer includes Yasmani Grandal and another player, reflecting the prior reporting of FOX Sports’ Ken Rosenthal that the backstop was in play. The talented 26-year-old would provide a platoon option with upside for the Dodgers.

Of course, with the Padres in the lead it still remains an open question just how likely Los Angeles is to move its star and, if so, how much money it is willing to eat on his contract. His market is complicated by the fact that several other right-handed power bats are available.