Cassielexa I think you are playing with fire. Unless this aquaintance at the gym is wanting to meet your husband too, it's seems dangerous. Out of respect for your husband, this aquaintance should not pressure you to meet up. What if the show were on the other foot and your husband perhaps wanted to meet up with a female, but not include you?
If you really have no interest towards this person in the romantic sense, and you want a friendship, maybe having an open discussion about it with your husband would be best as well as an invite if you decide to go out with the gym aquaintance.
Does that make sense?