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.
Few traders and brokers realize that the Letter of Intent is not a standard document in International Trade. When "LOI" is used, it actually refers to the Letter of Indemnity. This is standard usage of the term and has been for decades. The Letter of Intent (hereafter referred to as LOI) is often used in specific domestic trades, such as in real estate or corporate mergers, but it has no standard usage in International Trade itself.