The Catalan side have not received the full payment for the Sweden international's move last summer, despite the player since transferring to Paris Saint-Germain
The club's end-of-year financial report was presented by Faus on Friday, and it was revealed during a question and answer session that despite Ibrahimovic's recent move from Milan to Paris Saint-Germain, £6m of the transfer fee from the the striker's permanent move from Camp Nou to San Siro last summer is still outstanding.
The Sweden hitman initially moved to Milan on loan in 2010, and sealed a permanent deal the following summer after an unhappy single season in Catalonia.
And Faus also revealed that the Blaugrana would not receive any money from the player's recent transfer to PSG, but did disclose that the club received around £750,000 (€1m) for Thiago Motta's move to the Parisian club from Inter in January.
The vice-president also explained that the Catalan giants still owe Udinese just over £3m (€4m) as part of the deal that brought Alexis Sanchez to Camp Nou in the summer of 2011. That transfer included two add-ons, each worth around £1.5m (€2m), that were dependent on the number of games the Chilean started over the course of the 2011-12 campaign, and whether Barca reached the last-16 of the Champions League.
The supremo also made it clear that after exceeding last summer's transfer budget, Barca cannot afford to do the same again this time around.
"The club need to be cautious if they are to be able to take on ambitious future projects," he said.
"We have to look to the medium- and long-term stability of the club. Rational and austere measures need to be applied in order to secure a positive balance sheet.
"The club must reduce the debt to sustainable levels and, above all, not take on more debt. We have to prepare for what could happen in the near future and have stronger assets. For ambitious real-estate projects, we need a healthy balance sheet."
Barcelona's current net debt is thought to be around £260m (€335m).