Graham signed from Swansea City during the transfer window to provide competition for Fletcher, who has scored 10 goals for the Black Cats this season.
However, the Scottish forward has welcomed the signing of Graham, and admitted he's happy to move positions if O'Neill requires him to do so.
The 25-year-old told the Sunderland Echo: "I'm happy to play on my own up front, although I know not everyone is, but, for me, I quite like the added pressure of the extra responsibility. I quite enjoy it. But, having said that, I'm okay in any system.
"It's good to have Danny here. We've spoken with the gaffer about it and it's up to him to decide what formation that he wants to play. But at least now he knows that he has all sorts of options in terms of how to use me and Danny and Stephane Sessegnon.
"That's always good because not many managers have options, but I think he has them in abundance, so it's good for him and us."
Fletcher and Graham could both feature as Sunderland travel to The Hawthorns to face West Bromwich Albion on Saturday.