General Manager Brian Cashman traded Sheffield to the Tigers last November rather than give him a contract extension and trade another high-priced right fielder instead.
If the Dodgers were to trade Sheffield, he could demand a trade from his new team after the coming season.
The Yankees, who would trade Sheffield only if they were overwhelmed by an offer, would not agree to pay part of his salary, too.
Malone said today that he does not want to trade Sheffield, even though interest in the slugger has intensified in recent days.
But the run production the Yankees are sacrificing after trading Sheffield could be even more costly.
Strapped for cash in 1993, the Padres traded Sheffield to Florida, where he helped win a World Series in 1997.
Malone didn't spell it out, but the Dodgers know if they don't trade Sheffield and he remains unhappy, he could become poisonous on the team.
The Mets may have to entice the Dodgers to trade Sheffield, who hit .311 with 36 home runs and 100 runs batted in last season.
The Yankees traded Sheffield to the Detroit Tigers for three minor league pitchers yesterday, assuring that they have now become the most hated team in Sheffield's universe.
Dodgers General Manager Dan Evans said he was not trying to trade Sheffield unless a deal "makes complete sense to even explore."