Moeen made the allegation in his autobiography, which was being serialised in The Times newspaper, saying the apparent reference to Islamist militant Osama bin Laden came during his Ashes debut in Cardiff.
"We have followed up with the ECB (English board) and our team management and confirmed that the incident was investigated at the time, with a response provided to Moeen," a CA spokesman told cricket.com.au
"Moeen elected not to progress the matter any further and we have not been able to ascertain any new additional evidence through our enquiries.
"As such, the matter is considered closed."
England coach Trevor Bayliss had said that he spoke to his counterpart Darren Lehmann about the incident but the Australian player denied the claim, saying he said 'part timer' and not 'Osama'
"He's a very softly spoken sort of a bloke. He doesn't want to create too many problems for anyone. There were other players in the team who wanted to take it further but he talked them into not taking it any further."
According to Bayliss, there was no follow-up from Lehmann after he was told about the comments, and he did not feel the need to press the issue, as there were other significant things between the two sides that needed attention.
"Well I didn't get a response. I just left it with Darren to sort out one way or the other. I didn't hear any response, but everything was dealt with then.
"I'm not going to make too much of it. It was bloody three years ago, let's move on. (Cricket Australia) can do what they like I suppose - everyone has sort of forgotten about it and moved on since then. I don't see it as any real big deal.
"It was a hard-fought series…you're not party to what goes on out on the field and certainly nothing else was reported or anything through that series so we just left it at that," said Bayliss.
First Published: September 24, 2018, 4:52 PM IST