The local rivals will take to the field at the Riverside Stadium following their 1-1 draw at last month.
A solitary Frazer Campbell strike at the Stadium of Light was enough to avoid an upset last time around, and O’Neill is predicting a similar level of resistance from Tony Mowbray’s side on Wednesday night.
O’Neill told the club’s official website: "I thought Middlesbrough played very well against us in the first game, and that didn't come as any surprise to myself or the players.
"We know the game will be difficult; Middlesbrough have aspirations of returning to the Premier League.
"They are well enough positioned now in the Championship and the situation is very much the same as 10 days ago."
Despite coming through a hectic schedule over the festive period, the former Aston Villa boss plans to play a full-strength side in the replay on Teeside, with a fifth-round encounter with Arsenal awaiting the victors.
"We will go there as strong as we possibly can; obviously the FA Cup is a very important competition for the football club and its supporters," the 59-year-old added.
"I know Middlesbrough have had some injury problems but that was the case before they played us in the first game and it didn't affect them at all.
"They played very, very well against us at the Stadium of Light and I expect exactly the same again."