Under Wednesday's proposal, which addresses one of the key issues in contract talks, players would be subjected to one or more unannounced tests in 2003 to determine the level of steroid use. If the survey showed "insignificant" use, a second round of tests would be set up in 2004 to verify the results.
If more than 5 percent of the tests are positive in either survey, players will be randomly tested for two years.
The union did not say what penalties, if any, would be levied against players who test positive for steroids.
"We had an obligation to bargain on it. It was a serious issue," said union head Donald Fehr. "It took a lot of time and effort and thought."
Rob Manfred, the owners' top labor lawyer, characterized the proposal as "very significant," calling it "the kind of proposal that will put us very easily on the path to a very timely agreement" on drug testing.
He said a counterproposal could be given to players as early as Thursday. The plan the owners put forth in February called for far more extensive testing. Players would be tested three times a year for steroids and other performance-enhancing drugs, and once a year for illegal drugs such as cocaine.
Former MVPs Jose Canseco and Ken Caminiti admitted steroid use earlier this year, and Canseco estimated that up to 85 percent of all major leaguers took muscle-enhancing drugs during the years he played, 1985 to 2001.
Fehr wouldn't say how widespread support for testing was among players. USA Today reported last month that it surveyed 750 players in June and that 79 percent of those responding supported independent testing for steroid use.
Player reps discussed the proposal in a conference call Tuesday.
"When we had the conference call, not one person in this clubhouse debated whether or not to have drug testing," Dodgers player representative Paul Lo Duca said. "We want it. It's no big deal to us. It's going to be a pretty strict test, and that's the way it should be."
The NFL and NBA test players for steroids and illegal drugs. The NHL has a policy similar to baseball's, testing players only if there is cause. For example, a player could be tested if he is convicted of a crime involving drugs or enters rehab.
Under the baseball union's proposal, players could also be tested for illegal steroids if teams showed "reasonable cause."
"It is not a watered-down type of proposal," Colorado third baseman Todd Zeile said. "It is a legitimate proposal to try and do something."
Both sides also discussed minimum salary, benefits and debt control.
The union's executive board is to meet Monday in Chicago and could set a strike date for what would be baseball's ninth work stoppage since 1972.
Players fear that without a contract to replace the deal that expired Nov. 7, owners might change work rules or lock them out after the World Series. The union wants to control the timing of a potential work stoppage, preferring late in the season, when more pressure is on the owners.