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.
The LOI as it is now used is a misunderstood application of poorly informed brokers and traders. A more proper application based on established custom and practice in International trade, going back even to the old medieval "Law Merchant" (Lex Mercantilis) is: Buyer requests a quotation _ in modern usage this is an RFQ/Request For Quotation _ NOT an LOI. Seller may then reply with a Quote. Buyer confirms receipt of quoted prices, and requests an Offer.