US crude was trading up 34 cents at $41.99 a barrel at 0726 GMT, but was still down more than 10% since the start of November.
Internationally traded Brent was also up 34 cents at $44.95 a barrel.
A weakening of the dollar - which dipped against a basket of currencies on Tuesday - makes greenback-denominated contracts such as oil futures cheaper for those holding other currencies.
"If we saw selling of the dollar and buying of the euro, it could support oil prices and give us a bit of a rally," said Ric Spooner, chief market analyst at Sydney's CMC Markets. "It's really a bit of an ECB wild card at the moment."
The European Central Bank (ECB) is widely expected to cut interest rates on euro deposits and extend its quantitative easing program at a key meeting on Thursday.
Still, traders and analysts remained bearish about oil.
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In physical markets, Dubai crude fell to the lowest since December 2008, averaging $41.691 per barrel for November, according to price-reporting agency Platts.
OPEC's biggest producer Saudi Arabia, which heavily influences the group's policy, is widely expected to keep output steady despite declining prices.
OPEC made a historic decision last year to keep pumping oil to protect its market share against U.S. shale drillers and other producers, which resulted in a glut that sent oil prices spiralling.
"There is a real risk that we could see lower prices," said CMC's Spooner. "The prospects for demand-growth are not large enough to go into the supply overhang."
China's economy showed renewed signs of weakness, with its manufacturing falling to a three-year low, according to an official survey released on Tuesday. Japan's manufacturing accelerated, but was at low levels.
WTI crude could fall through $40 per barrel in coming weeks if crude oil stocks do not decline in line with seasonal patterns, ANZ said.
Hedge funds' bullish wagers on U.S. crude fell to a more than five-year low amid concerns that U.S. oil output is not falling fast enough to offset the global glut.
U.S. government data showed no meaningful decline in shale output despite falling rig counts, with supply exceeding demand by 0.7-2.5 million barrels per day.