An earlier deadline expired Sunday, The Himalayan Times reported.
The three-day extension comes as Nepal faces another round of political crisis since the Aug. 14 resignation of Prime Minister Jhalanath Khanal, who had been in office only since February. Khanal quit after failing to reach agreement with other party leaders on the consensus government.
If the various parties fail again, the next caretaker government would be chosen through a majority vote in Parliament, where no party enjoys a majority.
The main parties are the Communist Party of Nepal (Unified Marxist Leninist), Nepali Congress and the Maoists. Khanal leads the Communist Party of Nepal.
Even if an agreement on a consensus government is reached by Wednesday, it is not clear who would lead it.
Khanal came to power in February, after winning the support of the Maoists. The Maoists, led by Pushpa Kamal Dahal Prachanda, have held the most seats in Parliament since elections in 2008.
Nepaltimes.com quoted Maoist Chairman Prachanda as saying even if the new government is formed through a simple parliamentary majority it could work more effectively than the previous governments because there are no options before the parties other than to take the peace process and statute-drafting forward.
Nepal was a Hindu kingdom for more than two centuries before a 10-year Maoist insurgency ended with a 2006 peace deal.
The current constituent assembly has until Aug. 31 to have a new constitution in place to make way for a national government.
The main issue in the political squabbling involves a Maoist demand of rehabilitating and integrating about 19,000 former rebels into the Nepalese military and security forces, which other parties don't accept.