Gulfsands Petroleum was a marginal player in Syria's oil market prior to the conflict, extracting only 24k bpd in 2010 (6% of the market). Yet it's the most active international company in attempting to find a way to extract again.

The snapshot is from my forthcoming book on Syria's oil.

After the license of Delta Crescent [an American company permitted to extract oil from the same block (26) under the Trump administration] was revoked by the Biden administration, Gulfsands is now pressing for a "food-for-oil program," say Dan Wilkofsky and Amberin Zaman of Al-Monitor.

Source

I highly doubt the US would greenlight a food-for-oil program in Syria: it's bad PR for little economic benefit. This is partly why the oil sector has never been exempted from US sanctions anywhere in-country.

In a roundtable hosted by New Lines Institute today, I asked Ilham Ahmed, Executive President of the Syrian Democratic Council, about the possible oil deal. She said, "There's so much speculation in this area" and that nothing has been agreed.