Mr Papandreou will meet Greek President Karolos Papoulias immediately after an emergency cabinet meeting has finished.
He is expected to offer a coalition government, with former Greek central banker Lucas Papademos at the helm.
Mr Papandreou himself would stand down, the BBC understands.
Full story: Greek crisis: Papandreou ‘to offer to resign’
Update: Reuters’ Stephanie Ditta has tweeted that Papandreu will not resign, pending negotiations with leaders of the main opposition party.