Prime Minister Julia Gillard will hold her first meeting with independent candidate Andrew Wilkie on Saturday.
Mr Wilkie is set to win the Tasmanian seat of Denison, giving him a role in deciding which party should form a minority government.
He has already spoken to the prime minister, but will hold his first formal meeting with her in Melbourne on Saturday.
Mr Wilkie will meet the Opposition Leader Tony Abbott next week.
At this stage, the ABC reports Labor has 72 seats in the new parliament, the Liberal-National Coalition 73, the Greens one and there are three confirmed independents.
Greens MP Adam Bandt has indicated he will side with Labor.