
More precisely, the rumors were about a possible marriage between Thyra and Prince Alfred, Duke of Edinburgh, or Prince Arthur, Duke of Connaught.
Prince Alfred of Edinburgh and Prince Arthur of Connaught were their namesake sons, and besides were far too young for marrying Princess Thyra.
Another candidate for marrying Thyra was King Willem III of the Netherlands, but he was rejected because he was too old (he was 36 years older than the Princess).