Former Wales captain Speed who won 85 caps for the Dragons, has emerged as one of the favourites to take the vacant national team job and reports suggested the FAW are keen to interview him.
However, in a statement on the club's official website, Birch said: "The speculation is very unhelpful as Gary has only one thing on his mind at the moment and that is to prepare the team for the derby game against Barnsley at the weekend.
"Although unwelcome, the Welsh FA's interest is quite understandable as he's not only a Welshman but also a manager with a great future ahead of him.
"Gary has not been approached and there are no discussions planned. He has already stated that he is happy here and we are more than happy with him.
"This has become an intrusion into his and the club's preparations and we will not be commenting further."