The Sun says Bruce has been searching for a goalscorer to shoot the Premier League new-boys to survival next season.
Mphela, 28, has notched 46 goals in 110 games for Mamelodi Sundowns, and 23 in 47 outings for his country.
A bonus for Bruce is that he has a price tag of just £1million.
Mphela is renowned for his pace and strength and is keen to carve out a career in England, despite interest from Serbian giants Partizan Belgrade.
He said: "I want to progress and the only way to do that is to go to Europe."