Bennett, who has succeeded Steve McNamara in the hot seat, needs to find a new captain for the Four Nations Series after ruling Wigan loose forward Sean O'Loughlin out of his 24-man squad through injury and says he plans to make his selection before going into camp this weekend.
Burgess, the South Sydney forward who is back in the international rugby league fold after an ill-fated spell in rugby union with Bath and England, and Graham, the former St Helens prop who captains his current club Canterbury Bulldogs, are the obvious candidates.
"The captaincy will be out of a couple of players, James Graham and Sam Burgess," said Bennett in a conference call from his Brisbane home which was cut short by a fire alarm in the Super League headquarters at MediaCity in Salford.
"They're the two in the category when it comes to the leading contenders but I want to talk to the chairman (Brian Barwick) and Nigel (Wood) when I arrive this weekend to see who it will be.
"I want to hold off and see their views on that before I decide who it is. We all know their qualities - they're certainly the two leading contenders."
Warrington skipper Chris Hill would have been a candidate had Bennett opted to continue with an England-based captain but the coach says he will have no qualms about selecting from the eight-strong NRL contingent.
"I'm not looking at where they're based," Bennett said. "It's down to who is the best person for the job; they're the best two candidates with Sean not available. The country they play in is irrespective."
Graham has the advantage of being a club captain and also took over as England skipper on the 2010 Four Nations tour following the loss of Adrian Morley and led them in O'Loughlin's absence against Samoa two years ago.
Burgess, who has led Souths this year in the absence of Greg Inglis, has long been touted as a future England captain and, after being used as the face of the Four Nations in the RFL's poster campaign, would provide them with a public relations coup.
"It's great to have Sam back in Australia playing in our competition, let alone in rugby league at all," Bennett added. "He's a huge player in our game irrespective of the country he's playing in.
"It's great to have him back in the English side from my perspective too - he's inspirational and everyone looks up to him. I know how much it means to him to be back playing for his country."
Burgess will not be able to play in England's warm-up international against France in Avignon on Saturday, October 22, after receiving a one-match ban from his last appearance for South Sydney but Bennett says that will not influence his captaincy decision.
