The ambitious City Reds owner revealed he has made a decision on the successor to Phil Veivers in the aftermath of Salford's surprise 21-20 win over high-flying Huddersfield at the Salford City Stadium.
Former Great Britain boss Brian Noble and veteran Australian Brian Smith thought to be among the front-runners for the post, and Koukash said:. "I have made a decision but I'm keeping it to myself for now. I just want to make sure it's absolutely the right one."
He added: "It's going to be my decision only. Whoever I appoint, I just want to be comfortable with them and know that they share my vision.
"What I'm setting out to do is transform the club into one of the biggest in the country, if not the biggest, and whoever comes in, I want them to believe in that. I really want to see them committed and believe in what I am saying.
"It's unlikely to happen over the next week or so. It will be at least a week before it's announced."
Koukash, a wealthy racehorse owner, is expected to fly out to Dubai on Monday and any announcement is not expected before his return.
Neither Noble nor Smith attended Friday's match, which was decided by a late drop goal by Salford full-back Mark Sneyd.
"I'm certainly delighted with the performance and the result," Koukash added.
"We played very well against Saints last week so we might be turning the corner now."