It wouldn't be the Doctor's first cinema outing. Doctor Who And The Daleks came out in 1965 and Daleks' Invasion Earth: 2150AD came out a year later, both starring Peter Cushing. And in 1996 Paul McGann starred in a made-for-TV film simply entitled Doctor Who.
So what kind of Doctor would Depp make? Although the current Doctor Who, Matt Smith, is winning plaudits for his other-planetary charm as the alien we love to love, it's practically his first role. Depp, on the other hand, has years of practice inhabiting characters who are out of synch with reality and imbuing them with such humanity and demented charm that we're convinced - or want to be - that the world is crazy and they are not. So playing the man from Gallifrey probably wouldn't be a stretch.
If the fates had decided differently, Depp, who was born in Owensboro, Kentucky, in 1963 but grew up in Florida, would be best known as a rock'n' roller. His parents split when he was a teenager, and he lived with his mother Betty Sue, his stepfather, a brother and two sisters. A wild child, he "started smoking at 12, lost my virginity at 13 and did every kind of drug there was by 14". At 15 he dropped out of high school to chase fame as a musician. One of his first bands, The Kids, achieved some success, opening for Iggy Pop, Duran Duran and the B-52s.
The story goes that on a visit to LA with then wife Lori Anne Allison (married 1983-85), Depp, who was working in telephone biro sales, met Nicolas Cage, who encouraged him to act - although fans also owe a debt to James Dean, whose Rebel Without A Cause was another important catalyst.
An even more important meeting was the day that Depp encountered Tim Burton. As partnerships go, theirs has been wonderfully inventive. Depp has said: "He can ask me everything. If he wants me to have sex with an aardvark in one of his next movies, then I will do that." Well, we wouldn't put it past him...
They've made seven films, each more bonkers than the next, including Charlie And The Chocolate Factory, Corpse Bride, Sweeney Todd, Ed Wood, Sleepy Hollow and Alice In Wonderland.But the first, and arguably one of the best, was Edward Scissorhands, in 1990, the same year that Depp starred in Cry Baby, written and directed by that other genius eccentric, John Waters.
It seems but a small step from there into the Tardis, and it is easy to see how the part might appeal to Depp. Apart from animated kiddie films, which he adores watching with his little ones, Lily Rose, 11, and Jack, eight, he claims not to see many new films, but his knowledge and appreciation of classic film and television are vast.
Depp had two key mentors - Hunter S Thompson and Marlon Brando - the latter of whom advised him when he was buying a private island in the Bahamas, having had some experience in similar matters. And he is extremely close to his older sister, Christi Dembrowski, who runs his production company. About her he has said: "Basically, Christi has kept me alive. I'm really like a blind mole, and she just leads me around, making me do the right thing, or I'd just fall off the cliff. She's like Superwoman."
These days Depp has packed in the fags and practises yoga, but the 1990s were, despite a plethora of great roles, something of a disastrous period in his life. He was a serial proposer, getting engaged to Sherilyn Fenn, to Winona Ryder, to Kate Moss and to Jennifer Grey. Dark roles appealed to the darkness inside him. Drink and drugs, taken to anaesthetise, were constant companions.
Luckily, in the late 1990s, Depp met his partner, Vanessa Paradis, the French chanteuse-model-actress. It was a coup de foudre. "I first saw her across a room, just her back... I pretty much fell in love with Vanessa the moment I set eyes on her," he's admitted. "As a person, I was pretty much a lost cause at that time in my life. She turned all that around for me with her incredible tenderness and understanding."
Despite the distorting mirrors of celebrity, there's little doubt that Depp and Paradis are deeply committed - he learned French to be able to talk to her parents - and that their union goes from strength to strength. Fatherhood has been another great stabilising factor. In 2006, he revealed during an interview that it wasn't the death by overdose of his friend River Phoenix, outside the Viper Room nightclub which Depp part-owns, that put him on the straight and narrow, but the arrival of his daughter. "Anything I've done up until 27 May, 1999, was kind of an illusion, existing without living. My daughter, the birth of my daughter, gave me life."
Wonderfully complicated and quirky, not to mention talented, Depp is nothing if not surprising. Approached to star in a movie spun off from an amusement park ride, he said yes at once, without any questions. His star turns as Captain Jack Sparrow - a characterisation based partly on Keith Richards and partly on Pep le Pew - though it has lost him the respect of many critics, has won him a legion of young fans and he couldn't be more thrilled. "When I meet a ten-year-old kid who says, 'I love Captain Jack Sparrow'… that's real magic for me." All the more so, we suspect, because with his bad-boy reputation, he was initially thought too edgy for Disney, and the filmmakers had to fight the studio tooth and nail for the right to hire him.
Might the kid-friendly factor be enough to sway Depp to go into battle against the Daleks? Some die-hard Who-vers insist that it will never happen, that Depp's weirdness goes beyond the British eccentricity that is a fundamental part of the Doctor Who character. But strange things happen in the space-time continuum.