A quick google suggests he never did. In fact, the ONLY thinks brought up relate to comments by Morning Joe asking him - and Kerry saying he is not working on doing that. Joe proceeded to tease him that he didn't say "no". THAT led to a slew of articles suggesting he might be interested.
Kerry has run for President. If you look at the actual timeline - for ANY nominee, this would be the point where they would be at least speaking to backers, peers, etc There is no sign he is. Not to mention, he said in 2004, that he would not have run without Teresa's support -- which he had in both 2004 and again when he actively considered running in 2005/2006. Teresa has had had health problems and she is older than Kerry. I think he has very comfortably moved into the elder statesman role - proud of the many honors he has received.
Not to mention, he seems very engaged in what he is doing now. He clearly is enjoying working with students at Yale and having "Kerry Conversations" there with people he can get to come with ease. (Here's one that you might like to watch with Al Gore, who has similarly abandoned any idea of becoming President - https://news.yale.edu/2017/10/09/watch-livestream-vice-president-al-gore-kerry-conversation ) He also is doing a lot of work on climate change with companies - including a huge effort with Vietnam.)
Anyone who ever ran for President, especially one who wanted to be President for what he could do, would have a very tough time saying in a way that even people wanting a story would take as an unambiguous NO. However, I think he is proud of what he has done and looks happy with his life - even never winning the Presidency. Though obviously, if he could magically become President, he certainly would not say no, I seriously doubt he wants to put his family and his close friends through that again.
You might remember that in 2004, the NYT critiqued how he managed his campaign. I disagreed completely with them when they spoke of how he was more likely to ask PA governor Rendell his opinion of how a program he had some part of writing into law was working than about demographics and politics. Their opinion was this was a bad thing - my opinion was that it was a very good thing for a leader to ask. That and having staff do serious research on the true facts on the Medicare drug increase rather than just taking a potshot. They wrote that he then did not use those facts when he attacked -- as if that meant it was not a good idea to get them first. IMO, it means fewer times when you have to concede that you were wrong and you had a ready response if others asked the question that he asked staff to find the answers to.
To me, reading that years later, I realized that John Kerry - as talented politically as he was - is far more interested in issues and how government can help than in politics. From many talks and interviews I have seen, he is most engaged speaking about climate change or trying to make a more peaceful world -- or as a Senator how to get healthcare or how to create a small business program that helps people become more successful.
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