Boss Glenn Hoddle admitted both players were struggling to make the clash against Kaizer Chiefs at Newlands Stadium.
Defender Ledley turned his ankle over in our first pre-season friendly against Stevenage Borough while Bobby has picked up a slight groin problem, although he trained lightly this morning.
"We've still got Bobby Zamora and Ledley out, Lars Hirschfeld as well," said Glenn at a press conference following training at the Athlone Stadium in Cape Town.
"We're trying to get them fit but we're running out of time for Tuesday.
"Ledley's is dragging on, it's been almost two weeks now but Bobby's is just a slight groin problem that he expects to settle down. If he's not ready for Tuesday hopefully he'll be okay once we get back to England."
Bobby Zamora and Ledley King look unlikely to feature in our second tour match in South Africa on Tuesday night.