The Northern Irish international missed from the spot in the 12th minute of City's defeat to Swansea last Saturday but with main penalty taker Elliott Ward currently sidelined, Clingan has been told to carry on.
"I've got no problem with Sammy taking the next one we get," said Chris Coleman to the CT.
"I don't care who takes them as long as they stick them in the back of the net. "If you've got the bottle to step up, go ahead and take it - but you'll be judged on that.
"I'll have no qualms if Sammy picks the ball up next time; I'm quite sure he'll score because he's done it before."