Unfortunately you haven't provided enough context to answer your question. Here are my thoughts:
Discrete choice designs are meant to determine which attributes of a product are influential and can affect customer buying choices. This is usually done as a group of attributes (profile). Adding a ranking to this could make it overly complicated. It is hard enough for folks to be consistent with their choices when there are relatively few attributes. It gets more challenging as the number of attributes increase (see partial profiling).
However, don't be discouraged, you may be able to use an ordinal scale to evaluate attributes (realize Likert type scales are a subset of the ordinal scale where the scale is evaluating how well the respondent agrees with the "statement"). I will only provide a few words of advice:
1. You should consider the within respondent variation and consistency as well as the between respondent variation and consistency (you should build strategies to evaluate this into your design (see repeated measures or nested design strategies).
2. You should (must) include multiple respondents and their selection is critical to your ability to extrapolate the results (are they representative of the potential customer population?)
"All models are wrong, some are useful" G.E.P. Box
