The 34-year-old, plagued by injury over the last two years, is three wickets away from becoming South Africa's leading test wicket taker.
"I'm looking at trying to get into the third test, get back with the boys. It's been a long time - shoulder, foot, all that kind of stuff. Watching the cricket and seeing some of the things that are happening on the field, I just want to get out there," Steyn told local radio.
Steyn made a comeback after 13 months out due to shoulder problems when he opened the bowling in January's first test victory over India at Newlands, only to hurt his heel.
"I've had a bit of an unlucky one with my foot. It seems like every injury I get is really bad. I'm probably another two or three weeks away," Steyn said.
"I have to play one or two warm-up games. So hopefully everything goes according to plan, and by the end of next week, I should be back on the cricket field," he added.
Steyn's shoulder problems began in December 2015 and about a year later he broke his right shoulder and tore three major muscles during the first test against Australia in Perth.
He went home to Cape Town for surgery, followed by lengthy rehabilitation before he was gently eased back in Twenty20 action in November.
Steyn was due to return in the one-off test against Zimbabwe in December but on the opening morning of the day-night match he was ruled out with flu.
Steyn, whose test average is an impressive 22.32, can point to a prolific record at Newlands with 67 wickets in 14 tests. His tally of 419 test victims is just shy of Shaun Pollock's record 421 wickets for South Africa.
South Africa take on Australia at Newlands from March 22-26.
Australia won the opening match of the four-test series in Durban by 118 runs on Monday and the second test starts in Port Elizabeth on Friday.
(Reporting by Mark Gleeson; Editing by Ed Osmond)
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