Others have disagreed, arguing the founding father wanted a Muslim-majority but secular and progressive country.
The debate over the two competing and contradictory visions has intensified in recent years as the country reels from growing Islamic extremism and Taliban militancy.
At the heart of this debate are some public addresses of Mr Jinnah given around the time of the partition of India in 1947.
Transcripts of those addresses have been available in Pakistan.
The archives of state-owned broadcaster, Radio Pakistan, also contain cranky old audio recordings of most of those speeches, except for one: his address to the Constituent Assembly in the port city of Karachi on 11 August 1947, three days before the creation of Pakistan.
For liberals in Pakistan, it was a crucial speech in which Mr Jinnah spoke in the clearest possible terms of his dream that the country he was creating would be tolerant, inclusive and secular.
"You are free. You are free to go to your temples, you are free to go to your mosques or to any other place of worship in this state of Pakistan," Jinnah declared. "You may belong to any religion or caste or creed - that has nothing to do with the business of the state."
Documented evidence suggest that Mr Jinnah's words didn't go down well with the powerful and ambitious religious ideologues around him at the time, who then made sure the speech was virtually blacked out in the next day's newspapers.
Successive military governments in Pakistan were accused of attempting to downplay, even remove, the speech from official records.
By the time Pakistan embarked on a process of Islamisation and introduced tough new laws aimed at religious minorities in the 1970s and 1980s, the more controversial bits of that speech were largely wiped out from public discourse.
Jinnah was repackaged as an Islamic leader, rather than a westernised secular man he had been for much of his life.
Along the way, whatever audio recording there might once have been of that crucial speech disappeared.
Mr Jinnah's ideals for Pakistan were further muddled, as the country's hardliners began to question whether the founding father had indeed said those words in his address, was he in the right frame of mind or what he might have meant by them.
"It's a case of criminal, wilful destruction of our history," alleges Murtaza Solangi, the former director general of Radio Pakistan.
He cannot say with certainty whether Pakistan ever possessed the audio recording of the 11 August speech.
But based on his persistent inquiries over the last few years, he's come to the conclusion that "if Pakistan ever had a copy of the speech on tape, it was probably destroyed deliberately".
In his quest to trace the audio, Solangi contacted the BBC in London. He was told the BBC archive didn't have the 'Jinnah tapes'. He then contacted All India Radio (AIR) in Delhi. Indian officials told him they have the speech.
But it took the Indian authorities another two years before they were forced to release the tapes in public domain -mainly in response to a request by an Indian Muslim activist under the country's Right to Information law.
So, when the news came last week that All India Radio had handed over original recordings of two of Mr Jinnah's 1947 speeches to Radio Pakistan, it was seen as a breakthrough of sorts.
"The only difference is we now have them in much better, original quality."
The first of the two speeches handed over is believed to be Mr Jinnah's last address on radio within the borders of present day India. It was recorded on 3 June 1947, in Delhi.
The second tape consists of Mr Jinnah's well-known address to the Constituent Assembly in Karachi on the day the country came into existence: 14 August 1947.
It was recorded by sound engineers from All India Radio. They were invited to come to Karachi from Delhi because the country about to be born did not have radio stations equipped for such recordings.
AIR engineers are believed to have recorded both of Jinnah's speeches in Karachi: August 11th and 14th.
"They [AIR officials] initially told me they have the missing August 11th tape, but of late have become evasive about it," says Solangi.
"They have told others they don't have it. At the moment, we just don't know whether they have it or not."
Some in Pakistan suspect it may have to do with the dominant Indian narrative which paints Jinnah as the man responsible for large-scale Hindu-Muslim violence in the run up to the partition and the man who divided India.
But it's not entirely clear why, if the speech indeed exists, the authorities in India would hand over two of the Jinnah tapes, but not the 11 August speech.
"I doubt it's deliberate," says Raza Rumi, director of Jinnah Institute, an Islamabad-based think tank. "Given the red-tape in the Indian bureaucracy, I wouldn't be surprised if Pakistan's request for Jinnah tapes is simply stuck or lost in the system."
The recording of Jinnah's 11 August speech may be of great importance to students of history on both sides of the border.
But if ever found, could it really help Pakistan's seemingly marginalized liberals to win an argument with the hardliners and the religious right in reshaping the country's now deeply entrenched Islamic identity?
"It's not about trying to convince the religious zealots that Jinnah wanted a different kind of Pakistan," says Solangi.
"It's about correcting our distorted history and letting the people decide what kind of Pakistan they want."