"We're very close," he told the World Economic Forum in Davos.
"They're about to close a deal, if not today maybe over the weekend, preferably in January rather than February."
As he spoke in Switzerland, the Greek government was in talks with private creditors on a voluntary exchange of bonds that would wipe €100 billion off the country's debt of €350b.
Rehn said Greece would remain a special case and the private lenders would not be required to take losses on any other eurozone country's debt, thanks to plans for a better eurozone financial safety net.
Attention was also on the US economy, which grew by 2.8 per cent in the last quarter of 2011, the Commerce Department estimated, an improvement on the 1.8 per cent growth posted in the third quarter but below an average market forecast for a gain of 3.2 per cent.
Wall Street opened down, with the Dow Jones Industrial Average falling 0.39 per cent in early trading.
The broad-based S&P 500 slipped 0.25 per cent, while the tech-rich Nasdaq Composite dropped 0.02 per cent.
On Thursday, official data had showed that sales of new homes in the United States skidded in December, down 2.2 per cent from November, bringing to a close the worst year on record.
Only 302,000 new houses were sold during the year, the lowest level in records dating to 1963.
New claims for unemployment benefits rose to 377,000, although the four-week average, an indicator of layoffs, continued to head lower.
Asian stock markets mostly rose on tentative hopes Greece would be able to agree a deal with creditors on writing down some of its debt, traders said.
Greek Prime Minister Lucas Papademos and Finance Minister Evangelos Venizelos on Thursday resumed talks with banks and insurers on a major writedown to help the troubled country escape a devastating default.
The deal under discussion would see private creditors take a "haircut" of at least 50 per cent on the €200b in debt they hold.
Previous rounds of talks have snagged on the amount of interest to be paid on the remaining debt.