The Black Cats have scored just six league goals so far, with five of those coming from Steven Fletcher, but O'Neill has backed Gardner to get among the scoring.
"I feel that Craig should have ten league goals at the end of every season - regardless of the number of games that he plays," he told Sky Sports News.
"When I say 'regardless of the number of games that he plays', I mean of course assuming he plays upwards of 25 of course. It would be asking a bit much if he only played eight or nine times!
"But Craig's eye for goal really could be a tremendous asset for us. He has got a great shot, he gets into dangerous positions and he hits the ball as strongly and as truly as anyone in the Premier League."
The 25-year-old joined Sunderland from Aston Villa in 2011.