The two leaders had met on the sidelines of the East Asia Summit on Saturday in Vietnam's capital Hanoi.
Gillard had outlined the measures taken by Australia to revise rules and laws to prevent frequent attacks on Indians during her meeting with Singh.
The Prime Minister is expected to be in Perth in October next year for the Commonwealth Heads of Government Meeting (CHOGM).
According to AAP, Gillard's spokesman said that Singh was invited to extend his time in Australia for a separate official visit either before or after the CHOGM.
Singh is yet to formally accept the invitation, and the Indian High Commission in Canberra today declined to comment on the issue.
India is Australia's fourth largest export market and just over 4,00,000 people living here claim to have Indian origin.
The visit is expected to allay some of the concerns about the safety of Indian students here after a string of racial attacks.
Influx of international students had fallen by 30 per cent in the last financial year, mostly due to a drop in arrival of Indian students in the wake of much-publicised racial attacks.
It has also been affected by the strengthening of the Australian dollar and aggressive marketing by universities in the United States.