Yes you can, with a custom product.
First, you can do what Monica suggested - only I wouldn't go with a workflow. It is an overkill to my taste. I would create a new text column (possibly hidden / read only) and use a list item event handler on item updating / creating. you can use the multi line text field
SPField.GetFieldValueAsText to get the value without HTML decorations!
But, for your solution, allow me to recommend a product that does what you need:
If what you need is more information in the lookup than just 1 text field in order to make the selection (Say, title only doesn't identify the item and you need to see title + notes + status + created by + created date when selecting) - then a dropdown is just not enough for you.
In this case, I can recommend a product that does the lookup using a grid with checkboxes for selection: http://www.kwizcom.com/images/CascadingLookup/CascadingFilteredLookupField/ImageGallery/big/CLF4.jpg
This way, you can set up the lookup to show multiple columns including multiple lines of text columns when viewing or editing the item, but the lookup will still be tied to a simple single line of text column.
Search for "kwizcom cascading lookup plus" in google for examples, or visit: http://www.kwizcom.com/sharepoint-add-ons/sharepoint-cascading-lookup-plus/overview/