The Czech finance ministry said Havana had raised this possibility during recent negotiations on the issue.
Cuba owes the Czech authorities $276m (£222m), and if the offer is accepted the Czechs would have enough Cuban rum for more than a century.
However, Prague said it preferred to get at least some of the money in cash.
Havana's debt dates back from the Cold War era - when Cuba and what was at the time Czechoslovakia were part of the communist bloc.
Cuba now does not have much money but it does have lots of rum - hence this unusual proposal, says the BBC's Rob Cameron in Prague.
The Czech finance ministry said repayment was possible either with rum or pharmaceutical drugs.
But Cuban drugs lack EU certification, so repayment with a more traditional medicine - popular in the Czech Republic - may be easier to arrange, our correspondent adds.