Pinnock has completed a one-match ban and Norgaard has recovered from an ankle injury.
Captain Pontus Jansson has not quite shaken off an ankle knock so he will miss out again.
Mads Roerslev and Shandon Baptiste are still sidelined for the Championship high-flyers.
Newcastle boss Steve Bruce is likely to be without Federico Fernandez for the tie at the Brentford Community Stadium.
The defender, who tested positive for coronavirus amid an outbreak at the club, had to be replaced at half-time during Saturday's Premier League draw with Fulham because of fatigue and midfielder Isaac Hayden, who deputised amid depleted resources at the back, could stand in once again.
Covid-19 continues to restrict Bruce's options with Jamaal Lascelles and Allan Saint-Maximin understood to be among several unnamed players who have tested positive – Javi Manquillo and Fabian Schar have also not featured in recent games – while Bruce will check on a series of knocks from the weekend.
Goalkeeper Martin Dubravka is working his way back to full fitness after an ankle injury, but is not yet ready to resume.