The Denmark striker is on loan from Arsenal until the end of the season.
Bendtner was expected to miss the game against Everton after recently having sustained a knee injury in the win over Liverpool following a poor challenge by Martin Skrtel.
“The news on Nicklas is encouraging,” said O’Neill. “We had originally been expecting to wait 48 hours for swelling to go down around the knee before we could consider a scan.
“But the knee itself got much better in the 24 hours immediately afterwards, which looked good and it meant he felt quietly confident about doing a little bit of training yesterday.
“The very fact that he felt confident enough to want to try it out is obviously a good sign, but we just have to wait and see how it develops over the week and see whether there’s any reaction.
“You can never pre-judge a game, but it wouldn’t surprise me if the cup game against Everton is a tight affair and that being the case, you need players who can nick you a goal and players who can stop them going in at the other end.
“We had that at the weekend in what was a very tight game against Liverpool, but we were defensively very solid and we had players like Fraizer Campbell and Nicklas who always had the ability to be dangerous in attack.”
