The 56-year-old Italian is expected to take over at Manchester City, who sacked Stuart Pearce at the end of the season.
Ranieri took over at Parma in February and guided them away from the relegation zone and finished the season on 12th-place.
A statement from Parma said: “Claudio Ranieri has informed the club of his intention to leave his role as first-team coach.
“The club would like to thank him for the precious work he carried out, which resulted in keeping Parma in Serie A. We wish him success for the future.”
Ranieri told Italian newspaper Gazzetta dello Sport: “The Manchester City challenge reminds me of the experience I had at Chelsea where without spending £1, we built a good team.
“I created the Chelsea miracle from nothing. My achievement convinced Roman Abramovich to buy the club. Then, mountains of money came as well as a selection of top players.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.