Darren, 47, struggled to adapt to life after leaving the army and, as a result, was a regular at the top of Waverley Steps begging for change.
He contracted an infection as a result of long-term health problems while sleeping rough and passed away on December 17.
The Ancre Somme Association Scotland has begun an online campaign to raise funds to give Darren the send-off he deserves.
The crowdfunding page has already attracted £1,750 - with £1,500 raised in the past 24 hours.
Tommy Davidson, secretary of the association, said: “When we saw Darren’s story we were very passionate and knew we had to do something. Darren served in Bosnia and we feel we needed to do something to help.
“We have raised £330 so far but we are determined to raise the campaign’s profile and reach the target.
“We just want to do our best for Darren and his family. He deserves to be honoured and remembered for sacrificing his life for us all. Now it is our turn to give something back.”
Friends have left floral tributes at the entrance to the steps, describing Mr Greenfield as “good as gold”.
Mr Greenfield, known to friends and family as Dan, served with the Royal Tank Regiment in Bosnia during conflict in the 1990s, also spending time with the Royal Army Pay Corps and Adjutant General’s Corps.
Mr Davidson has contacted the association’s ambassador, Alexander Stewart MSP, to ask parliament for cross-party support to improve the care and support given to veterans once they leave the forces.
He said: “We need to make sure the people who serve our country don’t end up on the streets. They should get the support they deserve when they return.
“Everyone needs to play a part in changing the way we treat former soldiers.
“It’s a disgrace that they’re not treated as heroes. They should not end up on the streets like Darren did.”
To donate to Darren’s funeral, go to http://bit.ly/2G4bX1Z