Under the five-year labour deal agreed to in November 2011, the sides held discussions about a draft and MLB had the right to inform the union by Saturday if it planned to start one next year. If MLB had given that notification, the union would have had until June 15 to veto it.
The sides said Friday that talks had ended.
"At this time, the players are not prepared to accept an international draft," union head Michael Weiner said in a statement. "The MLBPA will continue to discuss with players and the commissioner's office the many issues facing its international members."
MLB began restraints on international signings last summer.
Since there will be no draft, the system of a signing bonus pool with penalties for exceeding thresholds will remain in place. For the period that began last July 2 and ends June 15, the threshold was $2.9 million.
For 2013-14, the thresholds are based on reverse order of winning percentage in 2012. The Houston Astros have the highest pool at $4,943,700 and the Washington Nationals the lowest at $1,846,900, resulting in overall less money available for international players without teams incurring penalties.
For both 2012-13 and 2013-14, a team's six-highest signing bonuses up to $50,000 will not count toward its pool, and bonuses below $7,500 will not be included.
Only players from the U.S., Canada and U.S. territories such as Puerto Rico are eligible for the current amateur draft, which started in 1965.
MLB said the parties couldn't agree "on some of the mechanics and procedures related to such a draft."
"The parties intend to continue to discuss international amateur talent issues," it said in a statement.