Reports from Scotland this morning say that the Ibrox side have studied the capabilities of and are ready to beat off interest from the Premiership and move for the pair.
It is believed Tottenham have invited SuperSport's Khumalo over for trials while Mamelodi Sundowns' Mphela has been linked with former Rangers manager Alex McLeish's Birmingham City.
But Rangers, who have already received permission to talk to Khumalo, hope to get in first after both players had been recommended by Rangers' manager in waiting Ally McCoist, who was in South Africa for the World Cup.
Ibrox manager Walter Smith confirmed on Wednesday night that the 23-year-old hard-tackling SuperSport defender, who has won 23 caps for his country, is a player he is considering seriously along with Mphela.
Smith said: "They are the right type and I think they could enhance our squad."
But Smith knows Khumalo - along with 25-year-old Mphela, who was top scorer in the PSL last season - are attracting interest from other clubs now Mphela has already made it clear he wants to leave Mamelodi Sundowns for a bigger league.
Mphela has had spells with Strasbourg - making his debut when he was 19 - and Stade Reims in France but believes he has regained his best form and wants to prove that in a better environment.
Mphela, who has scored 13 times in 31 internationals, was also named player of the year and Rangers have been attracted by the fact he has a physical presence up front and is capable of holding the ball up as well as scoring.