The paper says GSK, which is reportedly being advised by Lazard and Citi, is one of a number of drugs giants circling United.
Reporter Jamie Nimmo cites sources as saying the bidding could go as high as US$200 a share, valuing United at US$8.7bn.
Chaired by Martine Rothblatt, the transgender co-founder of satellite radio business Sirius XM, the company has five products on the market, four of which treat pulmonary arterial hypertension (PAH).
Rothblatt set up the business up 21 years ago to develop a treatment for her daughter, a PAH suffer.
The stock, after a strong opening, eased back a touch. At 9.45am, they were up US$10.82 at US$137.43 for a rise of 8%.