A Liberal source has told Australian Associated Press the West Australian MP would be a good choice, as he would restore respect for the role in the wake of the Bronwyn Bishop scandal.
Noongar, Yamatji, and Wongi man Mr Wyatt said he had "not been approached by any colleagues".
Wyatt represents the electorate district of Hasluck, located in Perth's outskirts. He received an Order of Australia in 1996 and the 2001 Centenary Medal for his work to improve the lives of Aborigines and Torres Strait Islander peoples, and health and education in Australia.
Bronwyn Bishop resigned on Sunday after it was revealed she had spent more than $5,000 in government money on a helicopter flight from Melbourne to Geelong in late 2014 to attend a Liberal Party function.
Mrs Bishop did not disclose whether she had spent $6,000 to charter a plane from Sydney to Nowra in 2014.
She said she would pay back the $5,000 she spent on chartering a helicopter in Victoria along with a 25 percent penalty.
The Australian Government's Finance Department has been investigating the claims.