The country has been surviving on rescue funds since 2010 and is anxious to draw a line under financial upheaval next year and be able to service debt itself.
It is seeking to create 4 new, benchmark size bonds, replacing 20 separate issues with a face value of around 32 billion euros (28.54 billion pounds). The move would smooth out maturities and add depth to a currently shallow market.
"They (Greek authorities) want to do it by early November, but there is not a final decision yet", a banker who requested anonymity told Reuters.
Greece, he said, was sounding out holders of existing government debt, including banks and funds, to gauge the likelihood of their participation in the project.
A fund manager in London confirmed that Athens is considering going ahead with the deal by November. There would be support for the swap from the bondholders, the fund manager added.
The 20 bonds were issued in 2012 in a voluntary scheme whereby private bondholders took a 53.5 percent haircut - or value reduction - on the nominal value of their holdings.
It was the world's biggest debt restructuring involving bonds with a total face value of 206 billion euros. Major holders included banks and pensions funds in Greece and abroad.
The size of each bond which will be exchanged is about 1.5 to 2 billion euros. They have maturities ranging from 2023 to 2042 and are well known as the "PSI bonds" as the transaction was then dubbed Private Sector Involvement.
Apart from those 20 bonds Greece has only a 5-year bond trading in the market that issued last July, the first since 2014.
The vast majority of Greece's outstanding 319 billion debt is held by official lenders, with only 40 billion euros trading in the market.
"Right now you are looking at a whole strip of issues, none of which have tremendous liquidity. So if you can focus the trading in a handful of issues, that could on the margin boost liquidity as well", said Robert Tipp, chief investment strategist at PGIM Fixed Income in New Jersey.
He said he would participate in the swap "depending on the levels".
Greece's borrowing costs GR10YT=TWEB have fallen sharply this year back to pre-crisis levels, as investors see the prospect of further bailouts diminishing as well as signs of economic improvement.
(Additional reporting by Abhinav Ramnarayan in London; Editing by Michele Kambas and Toby Chopra)
By Lefteris Papadimas and John Geddie