The British pharmaceutical giant is among several potential suitors for the company. Amylin has already rejected a $3.5bn approach from Bristol Myers Squibb, a fellow US drugs company that is thought to have made a renewed offer.
Other names that have been linked to a possible deal include US drug maker Merck, and Sanofi, the French pharmaceuticals group that employs 1,800 people in Britain.
For Astra, which on Sunday declined to comment, the purchase would enable it to replace sales lost on existing drugs when patent protection expires. The company is facing a looming “patent cliff” caused by a gap in the company’s drug development pipeline.