Draghi told the Süddeutsche Zeitung newspaper that he would be ready to come to Berlin to answer criticism from German MPs about his handling of the euro crisis.
"If the Bundestag invites me, I would be happy to come," he told the paper. "That would be a good opportunity to explain what we're doing."
But he is unlikely to be asked to make a speech in the chamber, instead he would probably appear before the parliament's budget and Europe committee - though no date has been set.
Bundestag President Norbert Lammert thanked Draghi for his offer and said he would do his best to find an appropriate format for a discussion with "particularly interested and engaged MPs."
Recent polls suggest that half of Germans mistrust the ECB president, which, Draghi said, makes his job harder. "I must do more to explain our measures," the Italian admitted.
The parliamentary faction of the Christian Democratic Union - Chancellor Angela Merkel's party - dismissed any talk of Draghi making a speech in the chamber itself.
"A big appearance in the plenum will not be announced, because that could easily be misunderstood as a sign that the ECB is becoming dependent on governments," a spokesman said. "But there is no reason there can't be discussion in front of specialist committees."
Draghi has been criticized recently for allowing the ECB to buy unlimited state bonds on high interest rates. He maintains these bonds will only be bought if strict conditions are applied.
Draghi also told the paper that the programme is already proving successful, and that global trust in the euro is increasing. "Fund managers are bringing their money back to Europe," he said. "That is good for the economy."