AstraZeneca has been looking at Medivation for the past six months and is looking very closely at making an offer, the newspaper said, citing sources and a senior health care banker.
In March, Reuters reported that Medivation had been working with investment bank JPMorgan Chase to handle interest from other companies in a potential acquisition, but it had no plans to sell itself.
San Francisco based-Medivation, which has a market capitalization of $8.4 billion, focuses on cancer treatment drugs.
Less than a week ago, the company rebuffed a takeover bid from French drugmaker Sanofi, Bloomberg reported.
AstraZeneca and Medivation said they do not comment on rumors or speculation.