The federal government says Australia will be one of the few major economies in the world to avoid recession if the government's economic plan is followed.
Dr. Lowe's appointment is set to expire in September.
A decision on whether his term will be extended beyond that point has yet to be made, with a review of the Reserve Bank due soon.
The government insists the housing Australia Future Fund will help address supply problems across the country, providing social and affordable housing, plus extra assistance for women and children fleeing domestic violence and to improve housing in Indigenous communities in remote parts of Australia.
But the Coalition and the Greens have raised reservations about the 10-billion-dollar fund.
The Greens say the legislation, as it stands falls short - claiming the 30,000 homes proposed to be built over the next five years are not enough, and the 500-million-dollar cap on funds to be spent each year is insufficient to successfully address the housing crisis.
The opposition has made it clear it will not support the current proposal.
Minister for Housing Julie Collins says constructive discussions and negotiations are continuing with representatives from across the parliament.
