A method and a system for establishing an approach to hover path for a rotorcraft enabling it to approach a mobile target and to hover relative to the target. An initial approach to hover path is firstly defined from measurements of the characteristics of the respective routes of the target and of the rotorcraft and also of the wind conditions to which the rotorcraft is subjected. During the flight of the rotorcraft, a required approach to hover path is determined in real time as a function of potential variations in the characteristics of the target, of the rotorcraft, and of the wind. Thereafter, the initial path is updated by the required path where necessary in order to guarantee safety of the approach to hover path for the rotorcraft relative to the target.