The Potters have put an offer to Birmingham for their highly-rated centre-half and hope the money on the table will be enough to push through a deal.
Blues have yet to offer their response, though, with it important to ensure that any agreement will benefit all concerned.
They would prefer not to part with Dann but, following relegation out of the Premier League and with interest in his services mounting, they look set to sanction a sale at some stage.
Stoke hope they will be the ones to strike a deal, with Pulis determined to bolster his defensive options ahead of the new season.
"We have made an offer which we think is a reasonable offer to Birmingham and it's now up to Birmingham to come back and let us know whether they will accept it or not," he told Sky Sports News on the Potters' bid for Dann.
"We have interest in other players and we will do our business the right way if we possibly can."
Stoke are also keen on Birmingham forward Cameron Jerome, but Pulis insists there are plenty of names on his summer shopping list that are not currently plying their trade at St Andrew's.
"It's not just them, we have made offers for other players and we are interested in other players," he added.
"We do our business at Stoke the way we think it should be done and that's with both clubs involved and we'll tell you after we've done it."