It is in talks with Indian-born businessman Yusuff Ali, who founded Abu Dhabi-based Lulu, one of the largest chains in the Gulf region, the sources said.
Discussions between PIF and Lulu began four to six weeks ago, one of the sources said.
It was not immediately clear how big a stake PIF is seeking to buy as discussions are at an early stage, or whether the talks would lead to a final transaction.
Lulu operates shopping centres, hypermarkets and other businesses with an annual turnover of $7.4 billion, according to its website.
It has operations in Saudi Arabia and other Gulf states as well as in Egypt, India, Indonesia and Malaysia.
PIF, which manages $360 billion in assets, declined to comment. Lulu's director of marketing & communications, V. Nandakumar, said in an emailed response that "as a policy we never comment on market speculations and media rumours."
Abu Dhabi state-owned holding company ADQ invested $1 billion in Lulu earlier this year, two sources familiar with the talks said. ADQ did not respond to a Reuters request for comment.
PIF is seen as a driver of the kingdom's Vision 2030 plan to diversify the economy, with the authorities aiming to turn it into the world's largest sovereign wealth fund.
The Saudi government wants to expand the kingdom's retail sector as part of a drive to create one million jobs by 2020.
PIF invested $500 million in e-commerce venture Noon, which shortly afterwards began operations in Saudi Arabia. It also invested indirectly in the IPO of Saudi mall operator Arabian Centres .
PIF was also approached by Reliance to buy a stake in the retail arm of Indian billionaire Mukesh Ambani's Reliance Industries Ltd.
The fund, whose board is chaired by Saudi Arabia's Crown Prince Mohammed bin Salman, has become a more active investor since 2015, taking a $3.5 billion stake in Uber Technologies and invested $45 billion in Softbank's inaugural technology fund.
(Reporting by Hadeel Al Sayegh and Saeed Azhar; editing by Jason Neely)
By Hadeel Al Sayegh and Saeed Azhar