Potters winger Pennant, who played for England under-21s but has never won a senior cap, is looking into the possibility of joining up with Giovanni Trapattoni's Irish squad after revealing he is eligible through his grandfather.
Pulis said: "A couple of years ago, if you had said there were international players playing for Stoke City, you wouldn't believe it. So if Jermaine is going to be another one, then fine, that is not a problem with me."
He added: "If Jermaine has any Irish connections and Ireland want him, he has been terrific for us and is a good player. We have a lot of players at this club playing international football now and I think it just shows the progression."
However, Pulis has already made it clear that he is not a fan of non-competitive international fixtures and thinks there would be a marked reduction in the amount that are arranged if national teams had to pay for their players' services.
"I don't like international friendly matches, and I've gone on record saying that," Pulis said. "I think for full-blooded games, where they are playing competitions, it is fantastic to represent your country.
"But what I think should be done is that if they want to play friendly matches and take players away for them, then they should pay the players' wages - and then you'll see how many friendly matches are actually played.
"I think they are played, generally, for income-based purposes as much as anything else.
"I find it hard to take when certain players are picked for certain countries who are flying halfway around the world to play a game against another country and then flying back, and we are paying their wages to do that. If it's a full-blooded competition, no problem - they can fly around the world twice and play. But for friendly games, I find it difficult to take."
The Republic of Ireland's next match is a Euro 2012 qualifier against Macedonia on March 26, followed by a friendly with Uruguay three days later.
Source: PA
Source: PA