We might be able to give a more precise answer if we knew what form these "requests" take: notifications, a browser pop-up, or...? But since we don't, here are a couple of guesses:
If it comes up when you are using a particular app, it may be an interstitial ad in that app (an ad that's supposed to appear between screens). In which case the only solution might be to try a different app for that purpose (unless there is a paid version which doesn't include ads).
Or if it only appears when you are web browsing it's probably one of the sites you are visiting (or their ad-hosting company). Mobogenie is particularly bad for trying to push itself this way.
If it comes up at random times, or not when using any particular app, it may mean that you have an app installed that includes "push advertising". That practice has now been banned from the Play Store, but if you have something which pre-dates that ban, or installed it from somewhere else, this is still possible. So I'd suggest using one of several apps which can scan for apps using "push advertising" or "push notifications". This will tell you which app is responsible for these ads, and you can then eliminate them by uninstalling that app.
There is another thread here, which gives you more details on what I said above:
http://androidforums.com/android-ap...s-unwanted-shortcuts-browsers-redirected.html