According to the ANSA news agency, Berlusconi, at a meeting with the leaders of the center-right parties, offered to nominate one "worthy" candidate, but did not name names.
After suggested that Mario Draghi, who is running for president of Italy, should remain prime minister.
Italy's presidential election is scheduled for January 24th.
Earlier, Brazilian President Jair Bolsonaro said he would not go to the inauguration of the new President of Chile, Gabriel Boric, which will be held on March 11.