"Progress is satisfactory, things are advancing in a positive manner," the official told AFP, declining to give a number of participants in the scheme.
Athens had said earlier that it was seeking participation from 90 percent of its debt bondholders in the rollover, which is an integral part of a new 159-billion-euro ($223-billion) bailout loan for Greece pieced together by the eurozone on July 21.
On Friday, the Greek official noted that the September 9 deadline only concerned eurozone banks and funds and had already been extended to early October to cover global institutions.
"Participation is satisfactory among eurozone institutions but the process continues," he said, adding: "We have some ways to go, we will have a clear image in early October."
Greek Finance Minister Evangelos Venizelos has already noted that the initiative is expected to be completed by October 20.
Greece hopes to reduce its crushing debt, currently at over 350 billion euros, by 26.1 billion euros by buying back or rolling over maturing debt, and from lower interest on an earlier 110-billion-euro bailout from the EU and the International Monetary Fund.
The Institute of International Finance, an organisation representing more than 400 banks and insurance companies, has said that private sector investors will contribute 54 billion euros from mid-2011 through mid-2014 and a total of 135 billion euros to the financing of Greece from mid-2011 to end 2020.
Under the plan, banks and insurance companies holding Greek sovereign bonds could swap them for longer-term ones, extending the repayment deadlines to give Greece breathing space and effectively reducing its debt.
Greek investor roadshows to the United States, Russia and Asia are also planned for late September.