The size of the contract with the financial insititution, which is likely to last for four years, could be worth between €350 million and €400 million, the same sources added.
In February, publicity material at the Parc des Princes ground said that the Paris club and the Qatar National Bank (QNB) had etablished links.
"There is a partnership project between Paris Saint-Germain and a Qatari financial institution for a sum of about €100 million a year," one well-placed source in French football told AFP, confirming details given by a member of the club owners' entourage.
PSG, which is owned by Qatar Sports Investments (QSI), said in response that it had "no comment to make on any contract", adding: "We will give details about our contracts as and when they're signed."
According to a document sent to AFP, the financial establishment in question wants to become PSG's shirt sponsor from next season.
The United Arab Emirates-based airline Emirates is the current shirt sponsor. It has had its name on club jerseys since 2006 in a €3.5 million a year deal that runs out in 2014, according to PSG.
Qatari investors would also like to have their name on the club's home ground, the Parc des Princes, although that name will stay, as the ground belongs to the local authority in Paris.
With new backing, PSG, which has spent nearly €250 million on transfers since QSI became owners in June 2011, is hoping to bring its finances into line with European governing body UEFA's Financial Fair Play system.
Financial Fair Play is designed to ensure that all European clubs live within their means, at the risk of financial penalties or suspension from competition.
PSG would have to give more details on the project at the next meeting of the league's financial committee before getting approval.