Definitely not. In a healthy marriage, there should be mutual respect and fidelity. Imagining or being involved in any form of scenario where your partner is in an inappropriate relationship with a stranger is unacceptable. It can cause great harm to the relationship and the emotional well - being of both parties.
One story could be about a wife who met a stranger on a train journey. The stranger was an old lady who shared her life story filled with travels and adventures. The wife was inspired by the old lady's tales and it made her think about her own life in a new way.
There is no evidence to suggest that such activities occur in a gym environment. Gyms have rules and ethics in place to maintain a proper and respectful atmosphere for all members. This kind of description violates the basic norms of a public fitness place.
First, try to stay calm. Then, initiate a serious talk. Explain that this behavior is disrespectful and harmful to the relationship. Seek professional help like couples counseling if needed. It's important to address the root issues that might be causing this inappropriate interest, such as dissatisfaction in the relationship or personal insecurities.