The union is concerned that disclosures about Palmeiro's drug test may have violated his privacy rights. The disclosures include the time frame within which Palmeiro failed his steroid test, and which steroid was uncovered in his system.
It's uncertain what could be done for Palmeiro to remedy the leaks. Union spokesman Greg Bouris said late last week that he would have no comment.
Baseball says it acted appropriately. "No information about this test became public until after Mr. Palmeiro's grievance was fully litigated and decided," Rob Manfred, baseball's executive vice president, said in an e-mailed response last week to a Sun inquiry.
The New York Daily News reported that the union will discuss the issue with the commissioner's office tomorrow and might file a grievance.
Palmeiro's agent, Arn Tellem, has also expressed concern about drug test details being made public, as have some major league players.