The Whitesands project would see the creation of a raised walkway along the waterfront area.
The scheme has been revised a number of times to address public concerns about the river view and loss of car parking.
Last year an estimate of project costs put the overall bill at between £15m and £17.8m.
The Scottish government would provide 80% of the funding for the scheme with the remainder coming from Dumfries and Galloway Council.
It has already approved nearly £4.5m towards the project which means it has a maximum of about £500,000 to find.
A report to the local authority will ask it to agree that the project be officially published and adopted as a flood protections scheme.
It cites a range of reasons for the increased costs which include:
The council has spent nearly a year refining the scheme which it said had produced a range of "positive developments".
Those actions include:
Councillor Colin Smyth said: "I am pleased that we are now at the stage to seek committee agreement to commence the formal process of publishing the Whitesands project as a flood protection scheme.
"It is unacceptable that the largest town in our region continues to flood.
"That is why all councillors agreed for a flood protection and regeneration scheme to be progressed for the Whitesands, demonstrating the need for change and putting an end to the regular flooding that has plagued our regional capital for too long."
He added that it was more than a flood protection scheme and could create a "high quality public open space" to encourage the use of the Whitesands.

Watson, 22, was seeded eighth in the tournament but lost 7-5 6-2 to the world number 101 in Seoul.
The British number one, ranked 46 in the world, converted just one of seven break points in the first set and the American dominated the second set.
Watson's early departure comes less than a month after her first-round defeat in straight sets at the US Open.

The Bantams went ahead on 43 minutes when Billy Clarke started and finished a move, linking up with Steve Davies who crossed for him to score.
But the Shrews levelled a minute after the restart with a messy goal.
Tyrone Barnett chased a long ball and his shot hit Rory McArdle before rebounding back off him and spinning into the net past keeper Ben Williams.

KPMG and the Recruitment and Employment Confederation (REC) reported that the rate of expansion in hiring employees sank to a four-month low.
The rate of growth in short-term jobs however had sped up since April, the report addded.
It suggested that companies needed time to "digest the election result", which saw the Conservatives win a majority.
The number of job vacancies made available also fell to their slowest in 2015.
Although starting salaries for permanent employees continued to grow, the pace of growth sank to its lowest since April's nine-month high.
Recruitment agencies reported that the pay of temporary and contracted staff also continued to grow, although at its slowest since January.
The availability of temporary staff saw its fastest drop in seven months, leading recruitment consultants to report difficulties in hiring suitable people.
KPMG partner Bernard Brown said: "The UK job market saw a slight slowdown in May, as those on boards took time to digest the election result and work out the ramifications for their business.
" The public sector continues to suffer, with pay growth rising by just 0.2% in the last reported quarter."
A major flood protection scheme in Dumfries is set to make a step forward but has seen its cost estimate rise significantly to £25m.
[NEXT_CONCEPT]
Britain's Heather Watson has been knocked out of the first round of the Korea Open by qualifier Nicole Gibbs.
[NEXT_CONCEPT]
Two goals either side of half-time meant a point apiece for Bradford and Shrewsbury in League One.
[NEXT_CONCEPT]
The pace of hiring permanent staff in the UK slowed down in May, according to a report.