keeping tabs
To watch a person or a situation carefully so that you always know what they are doing or what is happening.
"Why is he still your friend on Facebook?"
"I'm just keeping tabs on him in case he starts talking to another girl."
"I'm just keeping tabs on him in case he starts talking to another girl."
Keep Tabs On
To keep tabs on someone is to make a conscience effort to know what that person is doing. Often, the person does not know that you are keeping tabs on them. Typically it isn't as drastic as stalking the person, but it could be.
I always keep tabs on my EXes via Facebook to see what they're up to.