Coach Richard Pybus said he was happy with the player's progress but added that Anwar, who is playing in his third World Cup, had not been able to practice since bruising his arm in the nets last Tuesday.
"He's coming along quite nicely but we will have to take things one day at a time," Pybus told Reuters on Sunday.
"It (the elbow) is getting better each day but it is badly bruised and there is swelling and we have to get that down first.
"We certainly won't be rushing him back until he is 100 per cent fit."
Should the left-handed opening batsman be ruled out of The Wanderers Group A match, which is a re-run of the 1999 final, he is likely to be replaced by 21 year-old Taufeeq Umar.
The 34-year-old Anwar, holder of the world record one-day score of 194, has just been recalled to the team after a long spell in the wilderness in an attempt to bolster Pakistan's batting.
He has undergone knee and wrist surgery over the last year.
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