The United Nations inquiry into the 2005 assassination of former Lebanese Prime Minister Rafik Hariri is seeking a one-year extension.
Mr Brammertz says progress has been made
Chief investigator Serge Brammertz said the move would give the inquiry "a sense of stability and continuity".
In a report to the UN, Mr Brammertz said investigators had made considerable progress - although he did not go into details.
The current mandate is due to expire next Thursday.
The report says an extension would "offer assurances to staff".
It adds that Syria's co-operation with the inquiry "has further developed".
"Full and unconditional co-operation from Syria to the commission remains crucial," the document says.
Mr Hariri was killed in a massive car bomb in Beirut in February 2005 along with 22 other people.
Critics say Mr Hariri could not have been assassinated without help from Syria. His death triggered huge demonstrations in Lebanon against the Syrians.
Damascus denied involvement but eventually bowed to international pressure, pulling out its troops after nearly 30 years of military presence.
Mr Brammertz is expected to brief the UN Security Council on Wednesday on the latest findings.