I can see how, with the romance in so many of the dances, one could develop feelings for one's dance partner. However, that does not mean that you would be compatible beyond the dancing.
I've danced with a number of men I found attractive at dance classes where we were regulars. I enjoyed the feelings without letting myself make the mistake of thinking those feelings meant anything real. It was the dance and nothing else.
Now, if you simply cultivate the friendship, you will find out if there is anything there beyond the dance.
Make a point in asking the whole class, or a group from class to join you for coffee somewhere after class. If your partner is interested, they will jump at the chance and the coffee after class will become a regular thing.
In a casual group like this, you can chat and begin to get to know your partner and others beyond dance. There is every chance that getting to know people in the group like this will cool your attraction to your dance partner because you will see where you are not compatible past the dance itself.
No need for declarations until you know each other as friends away from dance. Further, getting to know each other as friends outside of dance will show you if your partner is interested in you at all and save you the embarrassment of saying anything at all.
Odds are good that outside dance friendship will cool the infatuation and you will be glad you did not say anything!