The southern African country's unity government between President Mugabe and the two formations of the Movement for Democratic Change (MDC) is broke and failing to meet its various financial obligations such as paying civil servants.
The unity government has resorted to diverting donated humanitarian funds to finance various state operations.
"The constitution making process will require substantial financial and human resources," Lovemore Moyo, Zimbabwe's speaker of parliament, said, adding that parliament was finalising on the exact budget for the process.
"It is my fervent hope that development agencies and other foreign organisations will take as much interest, if not more, as they took in the challenges that our country has been facing and contribute financial and material resources in support of the work of the select committee."
Mr Moyo on Sunday announced a 25-member committee drawn from both President Mugabe's Zanu-PF and the two formations of the MDC that will oversee the drafting of a new constitution.
Zimbabwe is still governed by the 1979 Lancaster House Constitution negotiated between the rebel Rhodesian government of Ian Smith and the two liberation movements, Zanu-PF of Robert Mugabe and PF-Zapu led by the late Joshua Nkomo.
The 1979 constitution that led to Zimbabwe's independence has since been amended a record 19 times. The drafting of new constitution is expected to lead to free and fair elections in 18 to 24 months once the supreme law is signed into law by the president.
Under the terms of a unity deal signed last year, the select committee that will steer the new constitution making process will embark on a four month consultation process after which a draft constitution shall be tabled to an all-stakeholders conference not later than February 13th 2010.
The draft constitution and the accompanying report shall be tabled in parliament before March 13th 2010.
The draft constitution emerging from parliament shall be gazetted before the holding of a referendum between the period between April 13th and July 13th 2010. If the draft constitution is approved by the referendum, it shall be gazetted within one month of the date of the referendum between July 13th and August 13th 2010.
The draft constitution will then finally be introduced to parliament no later than one month after the expiration of the period of 30 days from the date of its gazetting in October 2010.
Zimbabwe last held a constitutional referendum in 2000 where Zimbabweans rejected Mr Mugabe's constitutional proposal arguing that it gave him too many new powers.