During talks at the United Nations, UN envoy Matthew Nimetz presented a proposal for a compromise to envoys that will now be discussed in Athens and Skopje.
Nimetz said he will travel to Greece and Macedonia soon to discuss the proposed solution, which was not made public.
"I am very hopeful that this process is moving in a positive direction," Nimetz told reporters following the two- hour meeting at UN headquarters.
Macedonia is known as the Former Yugoslav Republic of Macedonia (FYROM) at the United Nations, but the Security Council acknowledged that this was a provisional name when it agreed to membership.
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"I view this as a good set of ideas, a compromise, and a package that both sides should feel comfortable with and lead to a dignified and satisfactory solution," said Nimetz.
Some of the solutions floated include using the name New Macedonia or Northern Macedonia, but Greek nationalists argue that there should be no reference to Macedonia at all.