The Eagles have been given a recent boost in their bid for Premier League survival thanks to two wins from Pulis's first three matches in charge.
Francis, who is now part of the Welshman's backroom staff, believes that there could be a number of new signings arriving at Selhurst Park in the New Year.
"Tony will obviously look at the players he's got and the players in the academy to see if there's anything coming through," Francis told talkSPORT. "Certainly you would expect him to do some business in the window, if possible, to strengthen the squad as a whole."
Palace are back in Premier League action on Saturday when they face London rivals Chelsea at Stamford Bridge.