"Do you think an Italian prime minister can take on extra duties?" Monti said at a joint press conference with visiting German Chancellor Angela Merkel when asked about the reports.
"I take any reference to me in this context as a sign of respect for Italy and its government," he added.
Current Eurogroup chief Jean-Claude Juncker earlier on Tuesday said Monti would be an "excellent" candidate for the post.
"If he decided to do it, he would naturally have my support," he said.
Juncker, who is also the prime minister of Luxembourg, has said he will not be extending his own mandate beyond June.
French daily Le Monde earlier reported that European Union president Herman Van Rompuy had put forward Monti's name to head up the Eurogroup, which brings together the finance ministers of all 17 euro area member states.