Horgan, who played in all three British & Irish Lions Tests against the All Blacks during the summer, sustained a shoulder knock in Leinster's 33-20 European Cup pool win against Glasgow last Sunday.
Llanelli captain Simon Easterby is still suffering from the broken nose he received in the Scarlets' 50-28 defeat by Toulouse on October 22. The Lions flanker trained with a cast on his nose and is rated extremely doubtful.
The absence of the Lions duo would severely hamper Ireland's chances of spoiling the All Blacks' 'Grand Slam' tour aspirations with seven squad regulars, including captain Brian O'Driscoll, already ruled out through injury.
O'Sullivan said: "We have two main injury concerns at the moment in Shane Horgan and Simon Easterby, so we have named 24 in the squad to allow them as much time as possible to prove their fitness before we name our team next week.
"Shane Horgan picked up a shoulder knock playing in the European Cup last weekend, but we are optimistic that he will be fit to play."
O'Sullivan whittled his squad from 31 players down to 24. Veteran Leinster prop Reggie Corrigan, Leicester Tigers lock Leo Cullen and experienced flanker David Wallace, as well as newcomers Jamie Heaslip, Kieran Lewis, Robert Kearney and David Quinlan have been released back to their provinces and clubs.
Three uncapped players remain in the 24-man squad - Ulster's Rory Best, Neil Best and Andrew Trimble.
O'Sullivan, who will confirm his starting line-up next Tuesday, added: "Training has gone well over the last week, and the new faces in the squad have fitted in very well.
"The other players who have been released will come back into the equation for the games against Australia and Romania."
Munster captain Anthony Foley is expected to skipper Ireland against the All Blacks in the absence of O'Driscoll (dislocated shoulder) and Paul O'Connell (fractured hand).
Ireland squad to play New Zealand in Dublin on November 12:
Backs: T Bowe (Ulster), K Campbell (Ulster), G D'Arcy (Leinster), G Dempsey (Leinster), A Horgan (Munster), S Horgan (Leinster), D Humphreys (Ulster), G Murphy (Leicester), R O'Gara (Cork Constitution), P Stringer (Munster), A Trimble (Ulster).
Forwards: N Best (Ulster), R Best (Ulster), S Best (Ulster), S Byrne (Saracens), S Easterby (Llanelli), A Foley (Munster), J Hayes (Munster), M Horan (Munster), M McCullough (Ulster), D Leamy (Munster), D O'Callaghan (Munster), J O'Connor (Wasps), M O'Kelly (Leinster).