Both men grew up in Port Talbot in Wales, and Sheen, who looked up to Burton as a youngster, wants to delve into the Who's Afraid of Virginia Woolf? star's history.
He tells Britain's The One Show, "He was a huge, huge influence... not just as an actor, but also just as someone who came from the town and did very well, because coming from Port Talbot, people not necessarily feeling that confident about people being interested in them (sic), so someone coming from there like Richard Burton, (was a) massive influence."
Speaking about the possibility of portraying Burton in a project, he adds, "It's a tough thing to play someone who does what you do but does it better. I don't mind tough! That charisma... you hear those tones, it's very hard to replicate that."
Sheen also admits he wants to create his own retrospective on Burton: "I believe there is a script, but honestly I would like to develop something myself one day because I think something that affected Richard was coming from a town like Port Talbot and then going to Hollywood. Once you've left a town like Port Talbot, (it's) very hard to feel like you totally belong again afterwards once you've done other stuff and also feel like you don't totally belong in Hollywood because you come from somewhere like Port Talbot.
"I think I kind of identify with certain aspects, so I'd like to explore that kind of thing."