Lib Dem MSP Alex Cole-Hamilton and Labour colleague Daniel Johnson will hold a meeting with the Dr Elsie Inglis Scottish Women’s Hospitals’ Trust.
The trust’s proposals would see a statue placed on the Royal Mile near where the surgeon - who set up 14 Scottish Women’s hospitals on the frontline in the First World War - established her first hospital at 219 High Street.
It follows the recent unveiling of a statue to commemorate suffragist Millicent Fawcett, the first to depict a women in Parliament Square.
There are more than 43 statues of men in Edinburgh city centre but only two statues of women - one of Queen Victoria and one of a female victim of apartheid.
Mr Cole-Hamilton said: “2018 is a year for celebrating women’s progress and it’s right that public art in Scotland keeps pace with the rest of the UK in applauding women’s contribution to public life.
“The imbalance in Edinburgh’s statues is staggering. Statues inspire people and there are plenty of inspiring Scottish women who are unfairly missing out.
“Elsie made a huge contribution to the war effort in WW1, to Scottish medicine as a whole and to women’s equality. She ought to be recognised as such.”
Mr Johnson added: “A statue to Elsie Inglis would be a fitting tribute to a great woman whose inspirational work in the First World War and as part of the suffrage movement should be recognised by her home city.
“There are hardly any statues of women in the capital, so it is time we started to put that right.
“I am delighted to be co-hosting this event, which I hope will bring fresh momentum to the campaign for a statue.”
Ian McFarlane, founder and chairman of the trust, said he hoped the meeting would “galvanise Holyrood MSPs and MPs, medical, nursing, educational and other relevant representatives to ensure the necessary support and financial backing for this Scottish monument, in the capital Edinburgh, which is of such fundamental and paramount importance”.