Zia suggested the ruling Awami League and her Bangladesh Nationalist Party could each choose five persons from among 20 former advisers, who were part of two non-party regimes that oversaw polls in 1996 and 2001, to create the proposed interim government.
The "most acceptable person" for the two parties could head the government instead of the incumbent premier and the current parliament would endorse the structure in the same way that the House elects the President and Speaker, she said.
"In her address, she (Hasina) asked the opposition to agree to an uneven competition keeping power in her own hand...this is a proposal of convenience," Zia told a news conference that was televised live.
According to Zia, Bangladesh witnessed two most credible elections under the non-party caretaker governments in 1996 and 2001 that brought the Awami League and BNP to power respectively.
Zia suggested that advisers or ministers from those regimes could be picked to run the interim government in a credible manner during the upcoming polls. She urged Hasina to take steps for talks on her proposal.
The proposals from the Awami League and BNP came amidst growing uncertainty about the fate of the election due to be held by January 25, 2014 and mounting tensions between the two parties.
In an address to the nation last week, Hasina suggested the formation of an all-party interim set-up.
"My proposal to the opposition party -- we can constitute an all-party government during election time (and) I am requesting the opposition leader to respond to my proposal," Hasina said.
Zia ruled out the possibility of contesting the polls if Hasina remained as head of the government. "If we go to the election (with Hasina remaining as premier), BNP would be affected...you have lost credibility among the people,” she said on Sunday.
The Awami League, which has a three-fourths majority in the current parliament, scrapped the caretaker system by amending the Constitution two years ago. It acted after the supreme court ruled that the system was contrary to the constitution.
The opposition organised violent protests against the decision, leaving scores of people dead in recent months. The BNP contended that polls would be fair and credible only under a non-party government.
But the Awami League insisted that the caretaker system had proved counter-productive as it was abused and it failed to protect democracy. It further said the system paved the ways for installation of army-backed regimes.
The uncertainty about the election has intensified concerns among international stakeholders. The US and Britain yesterday reiterated their call to political parties to settle their disputes over the polls through talks.
British envoy Robert W Gibson said, "We welcome the announcement of the Prime Minister and other indications from political leaders over the last few days that the door for dialogue is open."
Britain hopes "all sides will act with restraint and do everything possible to discourage acts of violence", he said.
A US Embassy spokesperson said, based on "indications", there was hope that the two parties were willing to engage in meaningful dialogue to settle their disputes.
US Secretary of State John Kerry wrote letters to top leaders of the Awami League and the BNP and UN chief Ban Ki-moon urged them to resolve the stalemate through a constructive dialogue.
Bangladesh: BNP leader sentenced to life imprisonment
Al Qaeda leader Libi pleads not guilty in US court
Nixon-led US let Pakistan Army commit genocide in 1971
Bangladesh: Lawmaker sentenced to death for 1971 war crimes
US commandos raid hideouts in Africa, nab top Qaeda leader