One would think if you two are spending time together, and you're a guy, they would assume just from observing you that you two have something more than a friendship. As parents of a daughter, they would be ultra-observant of any male person who gets near her. They would erroneously assume just about any guy would be a potential boyfriend for her, and if she's mostly seeing just you (i.e. not having a bunch of guys over all the time) then I would probably conclude that her parents already know.

Just be very respectful to her and to them and you should be fine. As for telling them about your relationship, you can if you want to; unless they already disapprove of your friendship with her there shouldn't be a problem.

This applies to most situations but with Muslims, depending on how "observant" they are, there could be a problem, if you're not Muslim or if you otherwise offend their religious sensibilities or if they are just extremely paranoid about their daughter. I'm afraid all situations are going to be unique, but generally speaking the Muslim part does make dating more difficult because of the rules and observance of the religion makes people do things which are, from my perspective, strange or restrictive.

Not meant to be judgmental, just observing differences.