Shawcross has always insisted he wants to represent England, but he has fallen out of contention over the last 18 months.
However, Coleman's desire to gauge his interest in pulling on the red shirt is tempered by the history that exists between Shawcross and Aaron Ramsey.
The Arsenal midfielder broke his leg in six places after a challenge by Shawcross in February 2010, and Ramsey ignored the defender's initial attempts to apologise.
Coleman has spoken to Ramsey about the possibility of Shawcross playing for Wales, and he said: "I had a conversation with Aaron when I was in Cardiff and it was very positive, but there is an issue there.
"The point is to play football and be successful, you don't have to be best mates. I don't have to talk to you as long as it works on the pitch; you don't have to be best friends.
"The best dressing rooms I have been in have been edgy.
"That's what I tried to tell Aaron, he is a professional at the end of the day and he wants what is best for Wales. He wants to be captain of a winning Welsh side.
"I can make it as nice for the players as I can, they can come away and have a good time, but if they are not winning what's the point?
"What's the strongest team we can get on the pitch? That's what it is about."