The firm's entire public affairs activity is up for grabs and pitches have been taking place this week. A decision is expected in the New Year.
Lilly currently uses FD for some public affairs work but the new brief is said to be much wider and FD is believed to have been invited to repitch.
UK government affairs manager Thom Thorp confirmed the pitch was taking place but declined to comment further. The drug company's products include anti-erectile dysfunction drug Cialis and depression treatment Cymbalta.