I think either "American interests" or the Americans' interest are correct.
"The Iranian regime is certain that in any case 2012 will pass peacefully. They assume the US will not attack for fear of soaring oil prices and because of the presidential elections. They do not believe we will attack without a green light from Washington. Therefore, it is in the Americans' interest to convince the Iranians that the US may attack, not to convince us not to attack."
No, you can't substitute "American interests" for "Americans' interest" in this sentence.
We would say something is "in my interest," not "in me interest." A possessive form is needed.