Platinum Stars were close to landing Mnyamane at the start of the month but Matsatsantsa's interest could see the Vaal-born midfielder remain in Tshwane.
"Mnyamane did agree terms with Platinum Stars but was still yet to sign on the dotted line," says a well-placed source.
"SuperSport United have since come up with a better offer. An announcement will be made soon."
Mnyamane's agent Mandla Mthembu confirmed his client is on the move but would not divulge details.
"The deal is 99 percent done but I can't reveal the name of the team."
Mnyamane was previously linked with numerous Absa Premiership teams, including Mamelodi Sundowns and Orlando Pirates.
AmaTuks agreed to release Mnyamane following their relegation to the National First Division at the end of last season.