The centre-back has made just one appearance for England in the 4-2 defeat to Sweden, but as that was only a friendly he is still eligible to represent the country for whom he played as a schoolboy.
Shawcross has always maintained he has no interest in switching, but Welshman Pulis believes the 27-year-old should realistically consider the move if he wants to play international football.
"I'm convinced he should be in the England squad and if that's not going to happen then my attentions would be turned to crossing the border," the former Potters boss told The Sentinel.
"If England don't think he's good enough, Wales certainly do
I know that for a fact.
"He would be joining a Wales team with a genuine chance of qualifying for Euro 2016, so there's some big games to be had if he made that choice.
"I still think his best years are ahead of him
I'd be disappointed if Ryan thinks he's reached the top of his performance levels because he has still to reach his peak and should become better over the next four or five years."
Wales, second in their Euro 2016 qualifying group, are in with a good chance of reaching their first major tournament since the 1958 World Cup.
Source: PA