The unnamed movie is to be produced by Scott Rudin, Mark Gordon and Guymon Casady, while Fincher (Fight Club) has met with Sony’s Amy Pascal to discuss the possibility of directing it.
But he said he would only take on the project if Bale, who was Oscar-nominated for his part in American Hustle, is cast as Jobs, who died in 2011 aged 56.
Fincher and Pascal had a slightly turbulent relationship during the making of The Girl With the Dragon Tattoo, but Pascal has faith in his filmmaker abilities and is inclined to keep him happy, according to insider information given to The Wrap.
Famous people and the actors who have played them
Famous people and the actors who have played them
1/23 Ashton Kutcher as Steve Jobs...
Kutcher played the US entrepreneur who brought the world the iPod in 2013's 'Jobs'.
2/23 ...and the real CEO of Apple
The real Steve Jobs died in 2011 from respiratory arrest. He has been described as the 'father of the digital revolution' and the 'master evangelist of the digital age'. Shame 'Jobs' received decidedly mixed reviews with Kutcher's portrayal much criticised as superficial.
3/23 Helen Mirren as HRH Queen Elizabeth II...
Mirren won the Best Actress Oscar for her performance as Queen Elizabeth II in 2007's 'The Queen'. Stephen Frears' film depicts the aftermath of Princess Diana's death.
4/23 ...and England's real monarch
'The Queen' received widespread acclaim, with Mirren invited to dinner at Buckingham Palace after the film's release. The English actress was unable to attend due to filming commitments in Hollywood.
5/23 ...and the real World War II codebreaker
Codebreaker Alan Turing relaxes with friends before his Bletchley Park days during the Second World War.
6/23 David Oyelowo as Martin Luther King...
Oyelowo won critical praise for his role as the civil rights activist in Selma, despite being snubbed by the Oscars for his performance.
Photo credit: Atsushi Nishijima/© MMXIV Paramount Pictures
7/23 ...and the real civil rights activists
US Baptist minister and activist Martin Luther King Jr was assassinated in 1968.
8/23 Eddie Redmayne as Stephen Hawking...
Redmayne won the Best Actor Oscar at the 2015 Academy Awards for playing the famed physicist in The Theory of Everything.
9/23 ...and the real theoretical physicist
Stephen Hawking is renowned in the world of science for his work on the theory of time.
10/23 Jamie Foxx as Ray Charles...
Foxx won the Best Actor Oscar for his performance as blind rhythm and blues musician Ray Charles in 2004's 'Ray'.
11/23 ...and the real soul legend
Charles was planning to attend the premiere of 'Ray' but died several months beforehand of liver disease.
Jean-Pierre Muller/AFP/Getty Images
12/23 Meryl Streep as Margaret Thatcher...
Streep won the Best Actress Oscar for her portrayal as Conservative prime minister Margaret Thatcher in 2011's 'The Iron Lady'. Her performance was widely-acclaimed and considered one of her finest.
13/23 ...and the real Iron Lady
Thatcher did not watch 'The Iron Lady' so had no comment to make on Streep's presentation of her. Her children Mark and Carol were unimpressed, saying the film sounded like 'some left-wing fantasy' prior to its completion.
Fox Photos/Getty Images
14/23 Naomi Watts as Princess Diana...
Watts took on the title role of the Princess of Wales for 2013's 'Diana' about the last two years of her life. The film was slated by critics, with The Mirror writing that 'Wesley Snipes in a blonde wig would be more convincing' as Diana than Watts. Ouch.
15/23 ...and the real Princess of Wales
Diana, Princess of Wales died in a Paris car crash in the summer of 1997. What she would have made of Watt's performance in 'Diana' is a question best left unanswered.
16/23 Lindsay Lohan as Elizabeth Taylor...
Lohan played Taylor in TV movie 'Liz and Dick' about the Hollywood icon's torrid relationship with Richard Burton
17/23 ...and the real iconic actress
'Liz and Dick' was panned by critics with comments including 'campy and overwrought' and 'an epic of pathetic miscasting'.
18/23 Daniel Day Lewis as Abraham Lincoln...
Day Lewis won the Best Actor Oscar for his portrayal of the former US president in 2012's 'Lincoln'. The film centres on Lincoln's efforts in January 1985 to pass the Thirteenth Amendment to abolish slavery.
19/23 ...and the real former US president
'Lincoln' was warmly received by critics, with reviews including phrases such as 'the most remarkable movie Steven Spielberg has made' and 'one of the finest historical dramas ever committed to film'.
20/23 Nicole Kidman as Virginia Woolf...
Kidman won the Best Actress Oscar for her role as post-War author Virginia Woolf in 2002's 'The Hours'. The film was highly-acclaimed and also won the Best Picture Oscar.
21/23 ...and the real 'Mrs Dalloway' author
Woolf was not alive to see the film, having committed suicide by drowning in 1941. But she might well have been impressed, with journalists describing the film as 'deeply moving' and 'amazingly faithful'.
22/23 Phillip Seymour Hoffman as Truman Capote...
Hoffman, who died in February 2014 from a drugs overdose, won the Best Actor Oscar for his portrayal of the 'Breakfast at Tiffany's' writer in 2005's 'Capote'.
23/23 ...and the real 'In Cold Blood' author
Capote died from liver cancer and drug intoxication in 1984 aged 59. 'Capote', and Hoffman's performance in particular, were praised by critics.
However, there is one small problem - Bale, who bears a strong physical resemblance to Jobs, has not yet been approached to play the role.
The Batman actor is taking a hiatus after completing filming for Ridley Scott’s forthcoming Exodus, in which he plays Moses.
The new biopic consists of three long scenes documenting some of Apple’s product launches, including the Mac, NeXT and the iPod.
Sorkin, who won an Oscar for penning Fincher’s Facebook film The Social Network, based his script on Walter Isaacson's authorised biography, which was itself based on more than 40 interviews with Jobs.
Last year, Ashton Kutcher played Jobs in a biopic simply titled Jobs. The film received tepid reviews and amassed only $35 million (£21 million) worldwide.
But Sony believes there is still demand for a Jobs movie featuring A-list names, with 2015 being set as a preliminary production date.