SNP Lothians MSP Shirley-Anne Somerville has written to Environment Minister Roseanna Cunningham, urging her to make the long-awaited anti-flood scheme a priority if there is any underspend when the books are balanced at the end of March.
Around 500 properties along the Water of Leith were flooded when the river burst its banks in 2000, but plans for new flood defences have suffered repeated delays and cost increases and the previous system of 80 per cent government funding has been scrapped.
Now the council has split the work into three phases, each understood to cost around 24 million, the first of which is scheduled to begin at Warriston in the spring.
Ms Somerville said: "I know times are tight financially for the government, but I'm making a plea to the minister that if she does have money available, we need to look seriously at this scheme.
"The public well understands the huge pressures on government and council budgets, but it's now over ten years since the flooding.
"Residents understandably want to see some progress.
"The estimated costs of the project have soared. The longer the project takes, the higher the cost to taxpayers and the greater the risk of flooding in the meantime.
"I think these are compelling reasons for the Water of Leith flood prevention scheme to be given top priority should it prove that there is funding available towards the end of the financial year."
Most government departments have some underspend at the end of the financial year, often due to projects which have been delayed.
Last month, opposition politicians voiced fears the Water of Leith scheme could be under threat after Ms Cunningham and Environment Secretary Richard Lochhead wrote a letter to MSPs warning that funding for flood prevention was "tighter than it has ever been".
The letter also said the public were "an equal partner in providing protection".
Ms Somerville said: "The minister is right to accentuate what people can do themselves, but when you are looking at how severe the problem is in the Water of Leith, that's beyond what any household or what any community can do for themselves.
"Yes, there are some times when people can help themselves, but this is not one of them."
A Scottish Government spokeswoman said: "We are aware of the issues at Water of Leith and look forward to receiving Ms Somerville's letter. We will respond in due course."