He told the Financial Times that the change could form a central part of a "quantum leap" in how the bloc is governed.
"Temporary suspension of voting rights is something that should be explored," said Mr Trichet.
The ECB wants to see independent monitoring of eurozone nations, combined with tougher sanctions against those who fall foul of the rules, to prevent a repeat of the financial crisis in Greece.
But Mr Trichet's proposal may be difficult to implement without changing EU treaties and the idea is likely to be opposed by member states.
Earlier this week, Konrad Becker, a financial analyst at Merck Finch, told Bloomberg that investors are still concerned about the sovereign debts of European nations, which is leading to an erosion of confidence in banks holding government bonds.
By Asim Shah