In a conversation like that, anything he says could be used against him. If he were to make a mistake about a time or date, you could be charged with "lying under oath." Trump also has a habit of speaking mind before he has fully thought through what he is saying. A slip of some kind is not only possible, by likely.
Robert Gate has been charged with lying to the FBI during an informal talk with a couple of agents who advised him that if was off the record and he did not need an attorney. But something he misspoke on (and the agents conducting the conversation have said was not a lie) is the ground for his charges.
You do not sit down and talk in a situation like this, President or not.
Protocol on this is that they submit questions in written form, and the President writes back - after his repies have been reviewed, researched, approved by his attorneys, etc.
He did not "sit down with Mueller" because he is smarter then that.