The International Monetary Fund (IMF) and the European Union are at odds on setting a target for Greece's debt by 2020, and the two sides are now 10 billion euros ($12.9 billion) apart, a Greek government official told Reuters.
In the wake of the report the euro rose past $1.29 to hit a fresh three-week high of $1.2908 in early European trade.
"The market is getting a bit confident that a Greek deal will be struck, which will remove one of the near-term uncertainties in the euro zone," said Paul Robson, currency strategist at RBS.
Euro zone finance ministers, the International Monetary Fund and the European Central Bank are due to meet again on Monday to try to close the gap, which is necessary in order to release emergency funds for Greece and keep the country afloat.
The potential for a Greek deal and signs lawmakers in the United States will eventually agree steps to avoid a fiscal crisis there have been behind a strong rally in share markets around the world this week.
"Besides Greece, there is a very good chance that we will, before Christmas, have a deal on averting the U.S. 'fiscal cliff'," Philippe Gijsels, head of research at BNP Paribas Fortis Global Markets in Brussels, said.
"These two positive drivers should make for a strong month of December, which traditionally is a fairly good month anyway. We remain buyers of the dips and continue to focus on financials, which will benefit the most from a Greek deal, and on technology."
MSCI's world equity index .MIWD00000PUS was up 0.2 percent on Friday at 326.80 points on course for a gain of nearly three percent this week. That will be best weekly performance since mid-September.
European stocks opened slightly firmer on the growing optimism over a Greek deal and are set for their best week in about 10 months.
The FTSEurofirst 300 .FTEU3 was up 0.1 percent at 1,103.93, although volumes were relatively light due to the half-day closure of U.S. markets after Thursday's Thanksgiving holiday.
London's FTSE 100 .FTSE, Paris's CAC-40 .FCHI and Frankfurt's DAX .GDAXI were also little changed, while U.S. stock index futures pointed to modest gains when Wall Street trading resumes for the shortened trading day. .L.EU .N
Earlier, MSCI's broadest index of Asia Pacific shares outside Japan .MIAPJ0000PUS rose 0.7 percent for a weekly gain of 2.6 percent, its best week for two months.
(Reporting by Richard Hubbard; Editing by Alastair Macdonald)
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