"There seems to be a lot of optimistic talk that we're hearing this week about further cuts," Wirth said in an interview with CNBC's Jim Cramer.
Both futures contracts increased by more than 3% earlier in a session that was jolted by the Federal Reserve's emergency interest rate cut, according to Reuters.
The Fed's rate cut was in response to growing concerns about how the coronavirus would affect the U.S. economy.
The outbreak has spread in the U.S. and in other countries around the globe, including Italy and South Korea. There are at least 91,300 cases globally, as well as at least 3,110 deaths.
Oil prices have been under pressure since the outbreak began in January, weakening the demand outlook for the year.
It's against that backdrop that OPEC and its allies will meet in Vienna on Thursday and Friday.
"We'll see how the meeting goes this week," Wirth said on "Mad Money." "Clearly demand is off with concerns about the coronavirus, and I look forward to seeing what comes out of the meeting."
OPEC is widely expected to cut production, but the question is by how much.
Ehsan Khoman, head of Middle East and North Africa research at MUFG, said his "baseline scenario" for production cuts is 1.2 million barrels a day. He said he expects it to last from the second quarter of 2020 until the end of the year.
"Anything below a million [barrels a day], then we could see a leg lower, anything with Brent hovering around the $40 mark," Khoman told CNBC earlier this week. "That's really disconcerting."
Shares of Chevron closed down 2.28% at $94.39 on Tuesday. The San Ramon, California-based company has seen its stock fall 22.65% in the past 12 months. The stock is 25.88% from its 52-week high of $127.34.