The gym is an open area where individuals attend to concentrate on their health and not necessarily to socialize. Due to it, it is always tempting to make advances to a person in a gym. Others may find it uncomfortable or intrusive whereas others believe that it is time and behavioral as well as intent based. This question is increasingly being raised as fitness spaces grow more social. It is not a yes or no but it depends on context, respect, and awareness that is even more important than the place itself regarding reception of an interaction.
Shared Purpose

The majority of the people attend the gym to exercise and not to be disturbed. Understanding that common ground assists in making achievable goals of interaction.
Reading Signals

Body language matters. Earphones, routine, or not looking in the eyes are likely to indicate that one would like to be left alone.
Timing Counts

Ceasing to listen to someone in between the set or when they are in full concentration can be intrusive. It would be more respectful to wait till a person has gone to bed or worked.
Respectful Approach

An assertive flirting is far apart with a courteous and short note. Owing or respectful language reduces the possibility of causing discomfort to a person.
Easy Exit

It is important to give a person an easy way to check out. When interest is not well returned, retreating at the earliest instance reflects maturity.
Frequency Matters

There are attempts that are made several times after no response. Being very different to the tenacious attention, one of the respectful approaches is very different.
Gym Culture

Various gyms possess varied vibes. Smaller community gyms can be social compared to big, busy gyms.
Gender Perspective

In most cases, unwanted attention in gyms is common among many women. It is good to know this fact to put into practice cautiousness and compassion.
Better Alternatives

Fitting out or discussing fitness or equipment is usually much safer than direct flirting. It enables free association.
Mutual Comfort

Only in case both individuals feel good, an interaction is appropriate. Whether it is welcome is determined by mutual interest and not merely intention.