The Brazilians had been linked with the former Jomo Cosmos and Manchester City striker, but following the signing of Edward Manqele this afternoon, they have now turned their attention elsewhere.
Sundowns spokesperson Kabelo Mosito says the club will not be pursuing Mwaruwari, who retired from international football in 2010 having scored 29 goals for the Warriors in 44 appearances.
"We are not talking to Benjani. We have not approached the player and we will not be doing so," he tellsKickOff.com.
Meanwhile, Wits coach Roger de Sa was cagey when asked on the progress the club is making in their bid to lure Mwaruwari to their ranks.
"We are still talking with him. The talks are going well, but I cannot disclose further details," De Sa tellsKickOff.com.
Benjani, who is a free agent after parting ways with English side Portsmouth, is eager to play in the South African top-flight, but has also not ruled out signing for a Zimbabwean club.