It is the first time that such a senior US official has indicated that there could be a definitive end to the programme, which the CIA has in the past called an effective counter-terrorism weapon.
The drone strikes target Islamist militants in Pakistan's semi-autonomous northwestern tribal belt, where Washington says Taliban and Al-Qaeda operatives pose a threat to Afghanistan and the West.
Kerry made the remarks in an interview with Pakistan state TV following a day of talks with the newly elected government in Islamabad, which demands that the drone strikes cease.
Asked if a timeline was envisaged for ending the strikes, Kerry replied: "Well, I do. And I think the (US) president has a very real timeline and we hope it's going to be very, very soon.