Wolves chairman Jeff Shi handed O'Neil a public vote of confidence on Thursday.
O'Neil said, "I couldn't care less who's linked to my job, it doesn't bother me at all. It's not been a consideration at all. I'm fine, I'm really enjoying my work every day and desperate to make sure we can turn this situation.
"Being able to rise from moments like this will feel very gratifying at the end and we know it's a season's work well done when we get to where we're going to get to.
"My focus in this room with you guys always gets taken to who might take my job, but my focus when I'm not in this room is always around getting every little bit out of the group.
"I feel we can do better, the players feel we can do better. We have a good opportunity from tomorrow's game to the end of January to impact on and off the pitch what the rest of the season looks like."