"I'm not running, it's not me, that's for sure," Mr Kerry confirmed in the interview.
He said he hopes that a US presidential nominee capable of leading the United States in a better direction will soon emerge.
Last month US President Donald Trump accused John Kerry of violating the Logan Act by talking to the Iranian government and discouraging them from negotiating a new nuclear agreement with the current US administration. Trump said that Kerry "should be prosecuted on that."
The Logan Act was established in 1799 by then US president John Adams. It bans private US citizens from having diplomatic talks with foreign nations.
John Kerry's spokesman rejected Trump's accusations by calling them "wrong". He also emphasized that Kerry had contributed to negotiating a nuclear agreement with Iran.
In autumn of 2018, Kerry admitted that he had several secret meetings with top Iranian officials in Europe, including the country's Foreign Minister Javad Zarif, to discuss possible ways to save the nuclear deal.
In May 2018 Donald Trump said the US was withdrawing from the Joint Comprehensive Plan of Actions (JCPOA), calling it the "worst deal in history". He added that Washington was re-imposing sanctions against Tehran and also announced secondary sanctions against companies all over the globe that have business ties with Iran.