Under pressure to shift away from fossil fuels and slash carbon emissions, Royal Dutch Shell is reviewing its assets in the largest U.S. oil field for a possible sale, people familiar with the matter told Reuters. U.S. listed shares of the No. 2 energy company outside of the Middle East jumped Monday the on news.Shell's holdings in the U.S. Permian Basin could be worth more than $10 billion, sources say. Shell declined to comment.Shell’s energy transition plan, one of the sector’s most ambitious, aims to reduce oil and gas output gradually and boost spending on renewables, hydrogen and low-carbon technologies.A full sale would mark one of Shell’s largest disposals in recent years and would further shrink the Hague-based company’s U.S. footprint. The company has agreed to sell all but one of its U.S. oil refineries. A Dutch court last month ordered Shell to reduce its greenhouse gas emissions by 2030, much faster than planned. Shell plans to appeal the ruling, its CEO said last week, but the company will also deepen emission cuts, a move likely to shrink its oil and gas business.Even if Shell does put its Texas shale assets up for sale, finding a buyer might not be easy. Projects in the Permian Basin are large scale and require constant drilling – which eat away at profits.