Wallace and Staunton are locked in a duel to see who will provide cover for first choice fly-half Ronan O'Gara over the coming months and in France next year.
O'Sullivan revealed Ulster back Wallace is in the driving seat after naming him on the bench for Saturday's clash with South Africa but insists the competition between the two remains fierce.
"We took Jeremy on the summer tour to New Zealand and Australia and sent Paddy to the Churchill Cup," he said.
"The only anomaly in the situation is Paddy has been playing at 12 for Ulster, but his main position is fly-half. He's played most of his rugby there.
"The positions are not a million miles away from each other anyway so I'm not that concerned that he's playing most of his rugby at 12. If you look at form he's just edged out Jeremy.
"But that's not cut in stone - it's subject to change. We do need to find a second number 10 in the next year, or even sooner than that. The two guys left jockeying for that position are Paddy and Jeremy.
"I'll keep an open mind but Paddy has edged ahead. That's based on form. It's nip and tuck between the two them. We all know that Ronan O'Gara will start in the number 10 jersey."
O'Sullivan has selected his first-choice side as Ireland seek to beat South Africa for only the third time.
The Springboks have left many of their established players at home so Ireland will enter the match favourites to repeat their victory over Jake White's side at Lansdowne Road two years ago.
But O'Sullivan insists the November internationals, which also include games against Australia and the Pacific Islands, are as much about developing a squad for the World Cup as winning.
"We need three good performances. I'm most disappointed when we lose and play badly," he said.
"I want the team to play well. Our history against South Africa isn't the best. But I think we can beat them if we play well.
"Hopefully we'll get three big performances while looking at other options to expand our squad. Three wins would be great."