If granted such powers, Riad Salameh would be able to provide official cover to banks who have been restricting dollar transactions since September without state authorisation.
His request to the finance ministry was made in a memo, which was shared by local media and confirmed by two banking sources.
The document requests authorities take legal measures to grant the central bank "exceptional powers" to impose "temporary measures" restricting cash withdrawals, transfers abroad, and other banking transactions.
Such a move, according to the memo, would help "regulate these measures and standardise them between banks so that they are implemented in a fair and equal way."
The finance ministry has yet to respond publicly.
Banks have since September arbitrarily capped the amount of dollars customers can withdraw or transfer abroad, sparking fury among clients who accuse them of holding money hostage.
Although no formal policy is in place, most lenders have arbitrarily capped withdrawals at around $1,000 (900 euros) per month, while others have imposed tighter restrictions.
"The main objective of the letter sent to the ministry of finance is to make the controls official," said one banking source who asked not to be named because he is not authorised to speak on the issue.
Banks' restrictions have fuelled panic in a protest-hit country suffering its worst economic crisis since the 1975-1990 civil war.
Sparked by a grinding liquidity crunch, the informal controls are increasingly forcing depositors to deal in the plummeting Lebanese pound.
The local currency has lost over half its value against the dollar on the black market.
The official rate was pegged at 1,507 Lebanese pounds to the greenback in 1997.
In an attempt to rescue their money, some customers have filed lawsuits against banks for trapping their savings.
Facebook groups have been established connecting lawyers to clients seeking to take their banks to court.
Several judges have ruled in favour of depositors.
Lebanon has been gripped by anti-government protests since October 17.
Although protests have declined in size, demonstrations continue, increasingly targeting banks and state institutions blamed for driving the country towards collapse.
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