The Black Cats have so far signed only Carlos Cuellar from Aston Villa and O'Neill, who is looking to bring Wolves striker Steven Fletcher to the club, wants to make sure there some other faces arriving on Wearside this summer.
"Unfortunately, I have been involved in late scrambles before, so it's nothing new to me in that sense," he said.
"Obviously, the most important issue is to try to get them in before the deadline finishes.
"Ideally it would be great to get them in and be part of the club before you kicked off the season, and we will do our utmost to do that.
"But unfortunately, I am unable to promise anything other than that we do have players in mind and we are trying our best to get them."