The English-born pair are available to represent the Dragons due to family heritage and education history.
Coleman had attempted to persuade them to switch allegiances in order to improve their international chances but both Stoke City captain Shawcross and Cardiff City centre-back Turner have declined Coleman's advances.
The Wales boss said: "There is no further conversation there and both of those avenues have been closed off.
"I talked to Ryan and had a good conversation with him and his dream is to play for England. He was very honest and sadly for us he wants to pursue his England dream.
"I totally understand and respect that and we shook hands and I wished him all the best. I hope he fulfils that dream and gets his England cap."
Wales begin their World Cup qualifying campaign with a double header against Belgium and Serbia in September.