The Germany international is to hold contract talks and complete a medical with a view to sealing a switch to the Premier League champions.
The Bundesliga club confirmed via their official website: "Ron-Robert Zieler has exercised the option in his contract and informed Hannover that he will travel to English champions Leicester City to have contract talks.
"In addition, the 27-year-old goalkeeper will complete the sports medical examinations in England."
Hannover managing director said Zieler would always be welcome to return to the club in future.
"We've always been aware that Ron would continue to show his outstanding qualities in the first division," he said.
"We wish him all the best for the future. Ron will always be welcome in Hannover."
Zieler has played nearly 200 times in his six years with Hannover since leaving Manchester United, where he never made a senior appearance.
The club were relegated from the Bundesliga this season after finishing bottom of the table with just seven wins from 34, thus activating a clause in Zieler's contract to allow him to look for a transfer.