Katsvairo trained with the KwaZulu-Natal side for a few weeks before returning home to Zimababwe for personal reasons.
"Katsvairo has not returned yet," Dlamini tells KickOff.com.
"We couldn't get hold of him. He sent us a message which I cannot disclose for now but what I can tell you is that we couldn't reach him even though we've paid everything for him. We have also tried to get hold of his manager but he was not answering his phone.
"According to our knowledge he [Katsvairo] is still here in Durban because he did admit that he received the plane ticket and the details, that was the last time we spoke to him. I don't want to say something to you that will link with the message that he sent us. As a club we can't speak on his position right now and as for what's next for him, his agent is the right person to speak on that. As for us we can do nothing, we are fine with the guy we don't need him anymore."
Katsvairo's agent Michael Ngobeni, of M Sport Management, says his client went home to bury his father.
"Yes, they [Kings] are not happy because they tried to get hold of him, he was not available. I was also looking for him, I could not find him," Ngobeni says.
"But I did find him later, he had a problem and I didn't know he had a problem. So we were all looking for him. So I managed to find him later but already they were angry you know. You know this is football; when a team wants a striker we get them a striker, understand? He is a good striker, he plays in Cosafa, he played for Chiefs.
"His father passed away and he went back home and came back. He was frustrated by all that. At the end of the day that's how he is."
This website has been informed that Baroka and Bloemfontein Celtic have also enquired about the player in recent weeks, but Ngobeni feels Katsvairo faces better prospects of game-time in the NFD.
"I wanted him to sign there because he can get game-time. There are two teams interested in him but Kings have an opportunity to be in the play-offs you know, which is good for him.
"Remember we don't just sell players like potatoes we look at a club because you could see they need a striker. But ja, he is currently here in Jozi, but I believe Kings are still preparing an offer for him.
"His father did pass away, that was for real. And Kings did buy him a ticket to Durban, we sent him the ticket, he disappeared - that's when I found out he had a genuine problem. I tried to phone them back.
"Yes, he was under pressure from other clubs but we had to give Kings first option. Remember he is someone who wants to revive his career, so with the experience he's got playing in the NFD will give him exposure.
"This boy is hungry for game-time, he wants to prove a point. All that Kings have to do is to come and close the deal."
Kings are second on the second-tier table with seven games left, 12 points behind Highlands Park.