As far as I know, all the players have remained extremely vague as to what they would seek or be prepared to accept if the UK were to leave the EU. Legally, I am not aware of any reason why the UK would automatically leave the EEA as well but for such a momentous event, that's not a very useful way to look at the issues. The future shape of the relationship between the UK and the EU would first have to be worked out at the political level and the treaties could then be changed accordingly.
Beyond the technical details, it might however be useful to consider what would happen to the freedom of movement itself. Switzerland for example is not even in the EEA but still had to implement it to secure its bilateral agreements with the EU. But the text approved by the 2014 referendum against “mass immigration” would severely restrict the freedom of movement for persons and it's still unclear how this will be resolved.
Even within this ad-hoc framework, it's difficult to see how the EU could weaken one of the cornerstones of the single market without endangering the whole thing. Or how an agreement like that could secure the consent of all member states.
At the same time, it seems that the people who agitate for a break with the EU and a significant part of the UK public are opposed to the freedom of movement for persons as such. If that was even on the table, would they be content with symbolically leaving the EU while the rules remain unchanged in this respect?
Whether the UK tries to obtain some changes from within the EU, chooses to leave the EU but not the EEA or simply leaves everything abruptly and negotiates from the outside, that's the big question.