Ramirez would provide power at third base, where the $21 million Juan Uribe experiment has run its course. Dempster would provide the rotation depth needed for a club that has already dipped into its thin farm system to replace Ted Lilly with Nathan Eovaldi.
Dempster also would allow the Dodgers to move Chad Billingsley into the bullpen, where he might flourish after failing to recapture his All-Star level as a starting pitcher.
There are other names the Dodgers are scouting -- Corey Hart, Chase Headley, Bryan LaHair, Michael Cuddyer and Cole Hamels among them. The goal is to find a power-hitting corner infielder, a proven starting pitcher and a left-handed reliever.
That's an ambitious to-do list for general manager Ned Colletti, who for a change has the financial wherewithal to take on another club's bad contract (hence the interest in Ramirez and his $31 million). What Colletti doesn't have is the depth of top-shelf prospects likely needed to land someone like Hamels.
"If there's a baseball deal to be made that makes sense, we'll be able to make it from a financial sense," Colletti said. "That said, we still need to find the right player and have our people outmatch anybody else's prospects. There's more than one box to check off."
After reportedly agreeing to deal Minor League pitcher Garrett Gould to Houston, only to be rebuffed by first baseman Carlos Lee's trade veto, Colletti has found the market typically slow in developing so far.
"It's the same as always," he said last week. "People take names and your number before the [All-Star] break and focus on who they can make the best deal with. Now, you pay $2 and get $1 back. We've moved some scouts around to teams we think will be in position to move players. You want to be as prepared as you can be."
The Dodgers seem determined not to include Eovaldi in any trade, but it's hard to find any other untouchable prospects in the farm system.
That even includes starting pitcher Zach Lee, who cost the Dodgers $5.25 million to be bought out of a two-spot role at LSU. He was recently promoted to Chattanooga to showcase his readiness against Double-A competition, although he has yet to be dominant.
There are some players that might be attractive to other clubs, among them pitchers Shawn Tolleson, Chris Reed, Ethan Martin, Allen Webster and Juan Rodriguez, as well as position players Joc Pederson, Alex Castellanos and Blake Smith.
Dodgers Deadline trades during the Colletti era have been all over the map. His acquisition of Manny Ramirez in 2008 is quite likely the greatest trade in Dodgers history and the best Deadline trade of all-time. Spare-part pickups like Marlon Anderson, George Sherrill, Jon Garland and Ronnie Belliard contributed to successful stretch runs.
But the Dodgers also have dealt away Carlos Santana, James McDonald and Rafael Furcal in Deadline deals. Santana looked like the best hitter to come through the Dodgers' Minor League system since Matt Kemp when he hit 27 homers last year for Cleveland, but he's slumping this year. McDonald was recently snubbed for an All-Star berth, but he's a legitimate National League Cy Young Award candidate this year. Furcal couldn't stay healthy as a Dodger and was dealt to make room for Dee Gordon. But in his first full season with the Cardinals, he was the NL's starting All-Star shortstop.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.