Komphela's charges have picked up seven points out of a possible nine in their last three league matches, and they're up to fourth on the PSL log.
However, media reports suggest that Amakhosi chairman Kaizer Motaung is not entirely pleased with the team's performance.
The club's hierarchy is believed to have demanded answers from Komphela and football manager Bobby Motaung on how they intend to turn things around at the club.
Komphela, 50, is in his third season with the Soweto giants and he's still waiting to win his first major trophy.
He reached two Cup finals - the MTN8 and Telkom Knockout Cup - in his first season at Naturena.
But things have not been the same since then, and if he fails to redeem himself, he could be on his way out.
Muhsin Ertugral, who is back in the country, has been tipped as a possible replacement for the former Bafana Bafana assistant coach should the Soweto giants decide to let him go.