With six to eight other teams interested in acquiring right-hander Ryan Dempster, a source told ESPNChicago.com the Los Angeles Dodgers continue to work toward landing the veteran Chicago Cubs pitcher, who started Friday night in a 4-1 loss to the St. Louis Cardinals.
The Dodgers have given the Cubs a list of names to consider in a Dempster trade, according to a source.
The Boston Red Sox also have made an offer for Dempster, according to another source, but it is unclear if he is open to switching leagues. He has spent his entire 13-year career in the National League.
Other interested clubs continue to believe the Dodgers are the favorite to land Dempster, a source told ESPN.com's Jayson Stark.
But Dempster, who has 10-5 rights, meaning he can veto any proposed trade, is open to any scenario the Cubs present him, according to a source. There is an open relationship between Dempster, president Theo Epstein and general manager Jed Hoyer that should make a deal easier to complete.
The Nationals are pursuing "four or five" veteran starters, including Dempster, but appear to be having trouble matching up with the Cubs on the pitcher and would need to "get creative" to complete a deal for him, a source told Stark.
The Cardinals have checked in on a number of pitchers, both starters and relievers, a source told Stark, but a deal between the Cubs and Cardinals would seem to be a long shot. Those two teams have made just two trades in the past 30 years -- a waiver deal 10 years ago that sent Jeff Fassero to the Cardinals and a 1995 trade that sent Todd Zeile to the Cubs.
The Braves also have talked about Dempster but would prefer a pitcher who would re-sign next season, a source told Stark. Most teams expect Dempster to return to the Cubs as a free agent after this season.
scoreless streak ended against the Cardinals in the first inning, when he allowed three runs.
The Cardinals hit four straight singles in a span of six pitches with one out against the right-hander, who entered Friday night's game leading the major leagues with a 1.86 ERA. Carlos Beltran and Yadier Molina each had an RBI single and Lance Berkman drove in a run with a groundout.
Dempster's streak was the majors' longest since the Phillies' Cliff Lee had a 34-inning run last year. It was the Cubs' longest since Ken Holtzman also had a 33-inning streak in 1969.
ESPN.com senior writer Jayson Stark and The Associated Press contributed to this report.