The 27-year-old previously indicated his desire to play for the Soweto giants, and as a free agent, he's now eligible to join a team of choice on a free transfer.
Jayiya worked with Steve Komphela at Maritzburg United in 2014, before moving to Mpumalanga Black Aces.
Amakhosi have already welcomed a few trialists, including Tanaka Chinyahara and Mahamadou Traore, and they are expected to decide on whether or not they will be signed in the next few weeks.
Chiefs are looking for players to help them bring back the good old days having gone two seasons without winning a major trophy under Komphela, and should Jayiya impress the technical team, he will be expected to give them a new dimension in the final third.
Jayiya, who can play as a right winger, is an experienced campaigner with over 130 appearances in all competitions since turning professional.
He made 29 appearances for City last season and found the back of the net on six ocassions.
Jayiya was also reportedly on the radar of Orlando Pirates, but as things stand, Amakhosi appear to be well ahead in the race for his signature.