The draft European Union text, seen by Reuters on Tuesday, also urges the bloc to develop a common approach to cryptocurrencies, including possibly banning projects deemed too high-risk.
In its current form, the document - which could be adopted by EU finance ministers next month - would escalate an EU regulatory campaign against cryptocurrencies, which have so far been only partly regulated in some EU states.
"The ECB and other EU central banks could usefully explore the opportunities as well as challenges of issuing central bank digital currencies including by considering concrete steps to this effect," said the draft, prepared by the Finnish EU presidency and subject to possible amendments.
Digital currencies like Libra - also known as stablecoins - are usually backed by traditional money and other securities, while crypto coins like bitcoin are not. Both are cryptocurrencies.
The draft text could be discussed by EU finance ministers on Friday, according to the agenda for that meeting, with a view to its adoption at their next gathering on Dec. 5. ECB board member Benoit Coeure said in September the bank should "step up" its thinking on a public digital currency.