New York's main contract, West Texas Intermediate (WTI) light sweet crude for delivery in March, gained 22 cents to $98.93 a barrel and Brent North Sea crude for March was up 20 cents to $117.40 in morning trade.
"Crude futures rose... on hopes that a deal to bail out debt-strapped Greece was near," said Phillip Futures in a commentary.
Greek government coalition talks on austerity measures ended on Wednesday with one remaining point of disagreement, the prime minister's office said. It added that it hoped for a complete deal to be reached by Thursday evening.
Representatives of the European Union, the International Monetary Fund and the European Central Bank, have been organising massive bailout loans for the debt-ridden country.
Greece desperately requires emergency funds from its eurozone partners to avoid defaulting on 14.5 billion euros ($19.2 billion) worth of payments to bond holders due on March 20.
Other analysts however cautioned against raising expectations too high.
"At present we await the outcome of a Greek meeting today but I wouldn't suggest anyone clears their diary for this," Justin Harper, head of research at IG Markets Singapore, told AFP.
"We've seen too many meetings and deadlines postponed, moved and cancelled altogether for people to get too worked up about this latest 'line in the sand'," he added.
Traders were also closely watching developments in Iran, where lawmakers backed unspecified "retaliatory measures" prepared by Tehran's oil and trade ministries against a European oil embargo.
"In our view, unless Iran is able to secure an alternative buyer, the decision is likely to remain in the form of rhetoric and a threat," Barclays Capital said in a commentary.
However the situation surrounding the country remained tense, "with the risk of miscalculation resulting in a messy military endgame rising", it added.
Western countries have accused Iran of seeking to develop nuclear weapons but Tehran has insisted its atomic programme is for civilian purposes.