Pair did not play in defeat to Stoke City through injury
The duo, who both missed the 4-0 loss through injury, were shown displaying their torsos in images on the Facebook page of Newcastle's Tup Tup Palace nightclub.
Pardew, who now faces a relegation battle with the Magpies, is not impressed with the players' antics.
He was quoted as saying by The Sun: "This is a situation I will have to look at. Certainly, it is not ideal on the eve of a match, even if you are not playing."
Ireland is currently on loan from Aston Villa, while Best has been given regular opportunities since the departure of Andy Carroll in January.