Of the 8 million barrels a day imported into the U.S. last week, Saudi Arabia probably supplied about 1 million barrels a day, said Kilduff. He said that could come down by 100,000 to 250,000 barrels a day.
"The Saudis understand the importance of changing optics in the U.S. and are following it up by continuing to signal that they are going to reduce shipments into the U.S.," said Helima Croft, global head of commodities strategy at RBC. She said Saudi Arabia's energy minister has made clear that reducing U.S. shipments was an option.
"It's a good time to reduce because they're going into seasonal domestic demand swings," said Croft. Saudi Arabia uses more oil domestically during the summer months for its utilities.
Oil prices cratered Wednesday, falling to a five-week low, after the EIA report showed a smaller-than-expected draw of 1.7 million barrels of crude but a bearish build in gasoline stockpiles of 2.1 million barrels. Brent fell 3.7 percent to just under $47 per barrel, and U.S. crude West Texas Intermediate futures dropped 3.8 percent, falling below the key $45 per barrel level.
Crude has been under pressure also this week after OPEC reported ramped-up supplies from Libya and Nigeria, while OPEC and Russia recently sealed a deal to extend their 1.8 million barrels a day in production cuts for another nine months.
"Libya and Nigeria popped up, but at what point is the market's focus? They're more focused on the U.S. What's hanging over this market is that the U.S. will continue to overwhelm everything," Croft said.
"Everybody keeps saying it's OPEC's fault, but ... which producer just pumped up production?" Croft said. U.S. production has been growing and increased in the last week to 9.3 million barrels a day from 9.2 million the week earlier.
The International Energy Agency says non-OPEC supply should grow by 660,000 barrels a day this year but will more than double that by increasing 1.5 million barrels a day next year, outstripping demand growth.
The targeting of U.S. inventories is not a surprise, as OPEC has said that traders look too much at U.S. data and that global inventories have been coming down.
"The U.S. numbers are more available than most other numbers, so sending less to the U.S., it probably helps the optics of this. But ultimately whether or not they're shifting supply between the U.S. and Asia. Let's say inventory drawdowns, even outside of the U.S., should start to take physical effect on the market," said Eric Lee, Citigroup energy analyst.
The next level to test could be $40.
Lee said he expects inventories to continue to draw and $40 is unlikely. "If you did see $40 oil, that would suggest customers would draw even more than they were going to draw and that means a bigger snap-up later this year. In terms of $40 oil over the next three years, I see more of a fundamental basis for that."
Watch: Kilduff says OPEC oil supply 'whisper talk' never came to pass