Zieler, who joined Hannover from Manchester United in 2010, is widely expected to seek pastures new this summer following his German club's relegation from the Bundesliga.
Leicester have moved to the head of the queue for the German international, who is said to be available for little over £2.5m in this summer's transfer window.
"Ron-Robert Zieler has exercised the option right enshrined in his contract and Hannover 96 has been informed that he will travel to the English champions Leicester City for contract talks," read a statement from Hannover.
"In addition, the 27-year-old goalkeeper will complete the sports medical examinations in England."
If the move is completed, Zieler is expected to be number two to Kasper Schmeichel at the King Power Stadium.