The position of "not" in a sentence

I recently heard on an interview: "... I try not to live my life thinking about money..."(meaning that this person was not looking for money in his life) and the following question came in my mind: Can i construct this same sentence on a better way?(it looks pretty odd for me)

My first thought was constructing it like this: "I try to live my life not thinking about money"

Is it wrong? How should i face sentences with this construction when adding a negative sense to it?

I already appreciate your help.