Three options that may work:

1. Use the 'Description for Pickings' Notes of a product.  These will be added to printed (PDF) picking documents and can give users a list of bins where product CAN be put.

2. Print each stock quant (bundle of product in a location) on the picking slip (PDF report).  This will give users a list of bins where product ALREADY IS. Something like:

<t t-if="pack_operation.product_id.product_stock">
    <tr t-foreach="pack_operation.product_id.product_stock" t-as="stock_quants"> 
        <t t-if="not stock_quants.reservation_id"> 
            <span t-field="stock_quants.location_id"/> 
            <span t-field="stock_quants.qty"/> 
        </t> 
    </tr> 
</t>

3. Code your own PUTAWAY strategy, that deduces the correct bin to use based on your own logic.  Odoo supports 'fixed single bin location' for product categories, but this is where you WOULD plug in your own custom strategy:

https://www.odoo.com/documentation/user/10.0/inventory/routes/strategies/putaway.html

There is a community module at https://apps.odoo.com/apps/modules/8.0/stock_putaway_product/ that uses this concept to create a fixed location for each product.