The Chester-born 24-year-old is eligible for The Dragons due to being raised in the country, having represented them at Under-15 level. But, an offer from Manchester United’s academy saw the centre-back move back to England soon after and he eventually represented the Three Lions at Under-21 level.
Shawcross has previously insisted that he will reject any call-up to the Wales national side as he hopes to play for England, but Coleman is seemingly undeterred.
“My job is to try and improve Wales,” Coleman is quoting as saying in The Sun.
“Ryan [Shawcross] is a good player who could strengthen us.
“We don’t have a huge pool, we have to make the best of what we have. We could look at Ryan.”
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Coleman also revealed that he intends to speak to current captain Aaron Ramsey before an approach for the Stoke man is made after the defender ruled the Arsenal midfielder out for nine months following a leg-breaking tackle in November 2010.
The two are yet to reconcile, with Ramsey reportedly choosing to ignore Shawcross's attempted apology at the time of the incident.
Coleman added: “I will have a conversation with Aaron [Ramsey] because he’s somebody I respect a great deal, he’s our captain and an important player.
“I won’t shy away from it because there are issues.”