The teenager couldn't help asking him.
"Where did you meet this Frank?" Asked his young customer curiously.
I would say yes, but would write it like this:
The curious teenager could not help asking the store manager, "Where did you meet Frank?"
You could add more to make certain that the reader knows the young person is a customer, but it is too much in one sentence.
You could add something like:
The manager smiled at his young customer and answered, "I met him at your football game, the same day I met you."
If by "this" you are trying to convey that you are suspicious of Frank, then again you need to put that in context.
The curious teenager could not help asking the store manager, "Where did you meet Frank? He's strange."