Balfour and the team had agreed to a two-year, $15 million deal earlier this week, but that was dependent on Balfour passing a physical. The team had been concerned with Balfour's shoulder problems.
Duquette said the team could sign another free agent, seek a trade or turn to a player already on the team to close games.
"We would never say never or close the door, but we're going to turn our attention elsewhere, Duquette said via the Baltimore Sun's Dan Connolly. "We do our due diligent process on all the players before we sign them. and part of that is a medical review."
The team is still looking to replace Jim Johnson, who was traded to the Oakland Athletics this month.