So, I've heard this one a couple of times so far, especially in formal contexts on BBC Radio 4 and other tv/radio stations. OED states you can only say it this way — /nɪˈgəʊʃɪeɪt/, providing no other options. However, it's rather popular to say it with an /s/ sound. Since I'm not a native speaker, I wonder why it's so. Is this some kind of a dialect or...I don't know. Also, there's a similar issue with the word 'issue', yet of slightly different genesis. Somehow, people like MPs and Theresa May have got an odd way of pronouncing it like /isju:/ and /iʃu:/ from time to time, shifting their articulation depending on whatever reason there is. Like, if Theresa May gives a speech in the Parliament, she goes /isju:/, and then, immediately outside the building, she answers to a reporter with /iʃu:/. What's the reason behind?
In a comment, John Lawler wrote:
I've heard native speakers use both /nə'ɡosiyet/, with /s/, and /nə'ɡoʃiyet/, with /ʃ/. It's a question of how far the palatalization of the original *t goes, and that turns out to be an individual (or speech group) decision, which means it's variable, and may be subject to sociolinguistic factors, like education, social class, age, gender, location, etc. I don't know of any literature on it, but I'm not a sociolinguist.
In some words there is variation between /s/ and /ʃ/ in a "palatalizing" context: before an unstressed /i~ɪ/ sound (the "happy" vowel) that is followed by a vowel, or before /j/ followed by an unstressed vowel.
This isn't an area where pronunciations differ consistently according to dialect: rather, each speaker may have a different pattern of pronunciation for each word.