They start away from home against Benni McCarthy's in-form City side on Wednesday, before hosting defending champions Wits on Saturday.
City are unbeaten this season and are on a high after booking their place in the MTN8 final on Sunday, thanks to a victory over the Clever Boys.
Komphela, who has a win record of 38,7% in his three seasons at the club, will be looking to get off to a flyer after the break, but the numbers show that he is sitting with a mediocre record of having won just 24 league matches out of the 62 he has overseen.
So far this season Amakhosi have played to a 1-1 draw with Bloemfontein Celtic and that result was followed by a 2-1 defeat to SuperSport United, leaving the side languishing in 14th position with just a point to show for their efforts.
Chiefs have drawn 25 league matches with Komphela in charge, sitting on a 40,32% draw record. They drew 13 in his first season and another 11 last term.
They have lost 13 games (20,9%) of the 62 league games.
Komphela will be under even more pressure if he does not get positive results against City and Wits.
Amakhosi will be without suspended central defender Mulomowandau Mathoho, who was sent off against SuperSport.