So let's look at a few misconceptions. Often in understanding International Business you have to unlearn many things first, much of the information out there particularly is inaccurate or worse dangerously ambiguous.
If what you want is a quotation or offer, then sending a letter of intent makes you look ignorant while requesting a quotation will generally at least make you look like you know what it is that you want. And what you want, after all, is a price quote. Hence you want to request a price quote, via a request for quotation.