Allardyce will no doubt be looking to strengthen in the January transfer window, and both Watford striker Deeney and Sevilla midfielder N'Zonzi are said to be high on his list.
However he also soon hopes to have all his absent players back in action so he can fully assess the Everton squad he inherited before the window opens.
"I think getting the players who are injured, getting them fit again, is a main priority before everybody starts talking about the January window," Allardyce said.
Summer signings Davy Klaassen and Sandro Ramirez have struggled to adapt to the Premier League, while the likes of Ross Barkley, Michael Keane and Leighton Baines are also out injured.
"I have to say, when I've looked at this season's history of games played, players getting injured, it's no wonder they have struggled in all honesty," said Allardyce.
"The number of fixtures early on in the season, the amount of games played in the Europa Cup and then the League Cup and the Premier League and injuries on top of that.
"The new players haven't been able, for me - especially the foreign players - to settle in and show what they can really do yet.
"So hopefully we can get more out of them and they can be more determined to show more than they have already because we'll need them going into the Christmas and New Year period, which is going to be another hell of a battle."