Am I misreading signals?

I would really like a female opinion on this matter.
Recently I’ve started attending a gym near my residence and it’s been great and I’m probably in the best shape of my life.
Over the last week, I’ve noticed a woman who attends the gym fairly regularly, starting to watch me.
Two separate instances have me wondering if I should strike up and conversation, or introduce myself and possibly ask her our for a drink.
The first time I was at the weight station and she walked by, looking at me through the mirror, she was watching me so I smiled and she smiled back. (I’m not the kind of person to read into things, but I’ll be honest and say she did catch my eye)
The second time, she was set up at a machine near the further end of the gym, opposite of me. The gym was fairly empty at this point. Every now and then I would glance around (cause after awhile I get tired of staring at myself) and I would notice her popping her head out from her machine and she would be peaking out, looking in my direction.

Now, I realize it’s not much and I’ll admit, I could just be reading into this, but does anyone think she might be interested (inb4 just ask and find out) I’m just curious what everyone’s opinion is.