Archer, who burst onto the cricket scene at last year's World Cup, pulled up with the injury in practice on Wednesday and was awaiting the results of the scan.
A buoyant South Africa will seek to drive home their advantage at a favourite venue as they host an England side facing a big selection question in the second test of the four-match series starting at Newlands on Friday.
Archer expert ache in his correct elbow following the 107-run defeat in Centurion and may now be despatched for extra analysis as England search to judge the extent of the difficulty, barely than play in Cape Metropolis.
Archer also did not train because of soreness in his right elbow and has also had a scan, according to a BBC report.
USA seeks denuclearisation agreement with North Korea
Spectators watch a musical performance during an event marking the new year on Pyongyang's Kim Il Sung Square on December 31, 2019.
Should Archer not be passed fit, and the current indications are that he is not expected to bowl on Thursday (today), England will be without their quickest bowler, who took five wickets in the second innings at SuperSport Park. Matt Parkinson, selected ahead of Bess in the initial squad, has slipped below Bess in the pecking order after struggling for control in England's warm-up fixtures in Benoni.
England batsman Jos Buttler admitted that he is not "performing to the standards" and said that he is trying to improve his game. In 2019, he played 11 Tests, scoring 502 runs at 25.10 and crossed fifty only thrice.
'I think since I've come back into Test cricket I've tried to trust my defence for longer periods. "But [playing my natural game] is certainly something I'm trying to work out", he added.
"For me moving forward I've got to play the situation, as I've said, but I will try to be a bit more positive".