The Scottish midfielder swapped Anfield for Stoke in the summer on deadline day and despite making his debut in the 2-2 draw with Wigan, has spent little time with his new team due to his international commitments.
Adam featured for Scotland in their two fixtures against Serbia and Macedonia and will now return to the Potters ahead of their match at home to Premier League champions Manchester City.
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However, the midfielder has yet to train with his new team-mates, much to his manager's frustration, with Pulis also hoping Adam did not pick up any injuries whilst featuring for his country.
Pulis told reporters: "He [Adam] only watched us in training the day before the Wigan match and then he was off to play for Scotland straight after.
"So he hasn't even worked with us yet and that is really, really frustrating with him being a new signing.
"I know these players are top professionals who can quickly adapt, but they are also playing against top professionals, so you want time with them on the training pitch to prepare.
"Hopefully, Charlie will come back to us fit and healthy on Thursday after his international commitments."