According to the daily, the meeting between Khan and US President Donald Trump is the culmination of hectic behind-the-scenes diplomatic efforts spanning many months.
Officials with direct knowledge of the efforts were cited as saying by the daily that Bin Salman used his personal contacts with Trump's son-in-law Jared Kushner to arrange the invitation for the Pakistani Prime Minister to the White House.
Kushner is also a senior adviser to the US President.
Efforts to arrange Khan's trip to the US began in December after Trump wrote a letter to the Pakistani leader, seeking his help in facilitating the Afghan peace process, the daily said.
An official, who is familiar with the development, told the Express Tribune that Khan was keen to have a face-to-face interaction with Trump because he was of the view that "such a meeting would help dispel many misperceptions the US President may have about Pakistan and its role in the region".
But given the apparent tensions in relations and the deepening trust deficit between the two countries, it was not possible to convince the American establishment for the Trump-Khan summit.
The only possibility was if Pakistan could bypass the US bureaucracy and make direct contact with Trump.
"That's when the idea of using an unconventional channel came," said the official, who requested not to be named since he was not authorized to speak to the media.
Pakistan then decided to approach the Saudi Crown Prince knowing his "close contacts" with Kushner.
Since assuming office, Khan has held several meetings with Bin Salman, something that helped him to develop a personal relationship with the future Saudi King.
According to the daily, the Saudi Crown Prince used his "good offices" to convince Trump through his son-in-law for a meeting with the Pakistani Prime Minister.
Another figure that complemented these unprecedented efforts was Republican Senator Lindsey Graham, who is considered close to Trump, said the newspaper.
According to it, Graham visited Islamabad in January and was "highly impressed' with the "vision" of Khan for Afghanistan and the region.
( With inputs from IANS )