The hearings will be rescheduled for next week unless the players reach agreements with their teams, which appears increasingly likely.
Players hold a 2-1 advantage over owners in the cases decided thus far, with Florida second baseman Dan Uggla ($5.35 million) and Washington pitcher Shawn Hill ($775,000) winning, and Tampa Bay catcher Dioner Navarro ($2.1 million) losing.
In addition to Santana and Aybar, 11 players remain scheduled for hearings next week.
Among the 46 players who swapped figures with their teams last month, Aybar had the smallest gap. He asked for $1.05 million and the Rays offered $900,000.