Clark, who is looking to reduce the club's wage bill, thinks a move abroad might appeal to King who is available on a free transfer.
33-year-old King, who was the Blues top-scorer for the past two seasons, has not featured in any of of the club's pre-season games.
Clark said: "He's been in the process of speaking to clubs for the last couple of weeks, home and abroad.
"My last conversation with Marlon was that he was very close to agreeing with one of those clubs.
"So we expect that to be concluded sometime this week. He gave us a certain time scale that it would be done and it was this week sometime.
"So when that's done, we will move forward and go again.
"I've let Marlon get on with it, I think a move abroad might appeal to him at this stage of his career, so it's what he finds best for him and his family.
"I've given him time off to sort out that side of it and I think Marlon himself is wanting a quick conclusion so he can get going with his new club," he added.