The Dubliner was given leave to return home to Ireland seven weeks ago due to a family issue and there have been suggestions that he will soon go back to England.
However, while Fahey has kept his head down after the club requested that his privacy was respected, inaccurate rumours have continued to circulate about the reason for his continued absence.
Clark addressed the matter after further theories were brought to his attention.
"There has been speculation with regards myself and Keith again," he said.
"It keeps rearing its ugly head and it's disappointing and frustrating because I have got a good relationship with the lad, we get on really well and I'm missing a hugely talented footballer.
"But I am missing him because, although football is very important to me, what goes on with my family is even more important and Keith has got an issue back in his homeland.
"And if I have got to keep saying it, I will – this is the truth. It is open-ended. When he comes back, it will be when Keith Fahey feels it's right to come back.
"And there's no way that, even if we had had a so-called bust-up, he would have gone because he would have been in breach of contract – and he totally isn't.
"He has got a situation that needs to be sorted out and sorted out in his own time."
"I think people have got to know me quite well here now and they know that I am open and honest," he added.
"And if there was a situation, I would just come out and tell the public.
"I am a fan myself, so I wouldn't like to think I was being misled. If there was a situation that needed to be rectified, I would do it."