Shawcross remains uncapped at international level, and received a solitary call-up to the Three Lions squad back in 2012.
Following John Terry's retirement from international football there is a defensive space to fill in Roy Hodgson's squad for next month's World Cup qualifiers against San Marino and Poland.
Pulis told The Sentinel that he believes Shawcross is good enough to shine for England.
He said: "Roy has managed in the Premier League, so he knows Ryan. If he thinks he's good enough for England then great, if not, that's up to Roy and is fine with me.
"Ryan just needs a chance. If he gets it, then brilliant and I'm sure he'll take it. If he doesn't, then he will just soldier on.
"I don't think it affects him. He hasn't been selected yet and his performances have been very good.
Stoke are aiming for their first Premier League win of the season when they play Swansea City this weekend.