Activist investor Elliott Investment Management LP has built up a more than $2.5 billion stake in Phillips 66, and is looking for the energy company to either sell or spin off its midstream unit to help boost its stock price.

Elliott Investment Management said on Tuesday it has built a stake of more than $2.5 billion in U.S. refiner Phillips 66, and plans to push for operational changes and the sale of the company's midstream business.

Phillips 66 shares are jumping 4% in intraday trading Tuesday following a report by The Wall Street Journal that Elliott Investment Management has built a more than $2.5 billion stake in the oil refiner.