Pennant was bailed pending further inquiries on Wednesday after being arrested for an alleged assault on a woman in a Manchester nightclub at the weekend.
The 29-year-old was was involved in a car crash two hours after the alleged assault and charged with drink-driving, driving while disqualified and having no insurance.
He will appear at Trafford Magistrates' Court next Wednesday to answer the driving charges, but Pulis says he could play in Stoke's game against QPR on Sunday.
Pulis will handle any disciplinary matters internally but has made it clear that he stands by Pennant and is keen to keep him at the club.
He was left out of Tuesday's 1-1 draw with Everton, but Pulis said: "The reason he wasn't involved was because of his hamstring. Hopefully come Sunday he will be involved.
"We've taken the approach that we will look after him. Once we know what he has or hasn't done, and what the court decide, we will deal with it.
"Do I want to keep him here? Yes, of course. He has another year on his contract. It's unfortunate it has happened and we have to deal with it.
"He has his court case on May 9. I've not spoken to anyone on the police force about it, so I can't comment. I'm certainly not going to hang the kiddie before we know what this is all about."
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