Lebanese depositors have been without access to their money since late 2019 as the country endures a severe financial crisis.
“Returning the funds to depositors is not impossible, and depositors should not have to wait for an extended period,” Mr Mansouri told Al Arabiya at the Arab Banking Conference in Riyadh during his first official visit to the Saudi capital.
Lebanese banks have imposed arbitrary restrictions on their clients since the crisis began.
The Lebanese government has estimated that the total financial losses exceed $70 billion.
Mr Mansouri did not give details of the specific mechanisms for facilitating the release of the frozen deposits within the banking system, now estimated at $90 billion.
“The Lebanese economy has declined from approximately $55 billion to around $20 billion,” he said.
He said the central bank, the Banque Du Liban, plans to provide a new exchange platform via Bloomberg to replace Sayrafa, which has faced criticism for a lack of transparency.
Mr Mansouri is the first governor to travel abroad since the start of the crisis.
He called ties between Lebanon and Saudi Arabia a “historic relationship”.
Saudi Arabia has regularly urged Lebanese authorities to implement reforms. It is part of a five-nation group, alongside the US, France, Qatar and Egypt, that supports a consensus-driven dialogue to address the prolonged presidential vacancy.
Lebanon has been without a president since October, with the divided parliament failing 12 times to elect a successor to former president Michel Aoun.
Saudi Arabia will “always play a positive role” in helping Lebanon to overcome its financial woes, Mr Mansouri said.
He assumed office after succeeding embattled former governor Riad Salameh, who left his position on July 31.
Many have blamed Mr Salameh for being the architect of a system that ultimately collapsed, plunging 80 per cent of the population into poverty.
Mr Salameh is under investigation in Lebanon and several European countries for alleged money laundering. He has consistently denied all charges against him.
‘We will not fund the Lebanese state'
Mr Mansouri said the central bank would stop financing the government.
“Our decision is final not to fund the Lebanese state, neither in lira nor in dollars,” he said.
This policy was a pivotal component of his inaugural plan, presented during a press conference on August 25, where he emphasised that any government financing requests falling “outside the legal framework” would be declined.
This marked a significant shift from a three-decade-long policy in which the central bank generously financed budget deficits without imposing conditions.
On Saturday, he told Asharq Al Awsat that if reforms are not passed, he will not lend funds to the state.
The failure of the country's political elite to implement reforms requested by the International Monetary Fund has hindered access to $3 billion in aid.
Addressing the issue of depositors' funds held in Lebanese banks since the crisis started, Mr Mansouri said: “People cannot be treated the way they are being treated now. This is a lack of respect for them and for the state.”