WTI last week reached US$62.21, the highest since May 2015.
February West Texas Intermediate crude was up 25 cents, or 0.4%, at $61.98 a barrel on the New York Mercantile Exchange.
United States crude stockpiles at the Cushing, Oklahoma, pipeline hub probably fell by 1.5 million barrels last week, according to a forecast compiled by Bloomberg.
Yet, surging USA production could offset some of the cuts from OPEC producers, as US production rose to 9.78 million barrels a day (MMBPD) in the latest week, according to last Wednesday's report.
Many producers, still suffering from a 2014 price collapse, are enjoying the rally, although they are wary it will spur rival supply sources.
Traders and analysts surveyed by The Wall Street Journal expect government data due Wednesday to show crude stockpiles declined on average by 2.5 million barrels in the week ended January 5, which would mark the eighth consecutive week of inventory draws if estimates are accurate.
"The US oil price is now into a range that is anticipated to attract increased shale oil production", said Ric Spooner, chief market analyst at CMC Markets in Sydney.More news: Golden Globes: 'Big Little Lies' Wins Best Limited Series
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Adding to the positive sentiment, analysts expect global economic growth to lead to higher demand for oil.
Supply reports this week from industry group the American Petroleum Institute and the US government's Energy Information Administration are expected to show USA crude stocks fell 3.9 million barrels, an eighth week of decline.
Crude oil futures continued to surge Tuesday on expectations the global oil market will soon re-balance. OPEC and 10 members outside the cartel agreed late last year to extend an accord to hold down crude output by almost 2% through the end of this year.
Nationwide output will average 10.85 million barrels a day next year and 10.27 million this year, both surpassing the prior record of 9.6 million pumped in 1970, the Energy Information Administration said in its monthly Short-Term Energy Outlook, which included the first estimates for 2019.
Rising U.S. production and weaker refined products demand weighed on the market, traders said.
However, some analysts believe market participants are getting to optimistic, especially given expectations for an increase in US shale production.
Gasoline futures gained 2.5% to $1.8362 a gallon and diesel futures rose 1% to $2.0662 a gallon.