If he explicitly asked to go to represent his country at the Olympics, I would've just let him. Making / keeping your key player happy is more important than him (not) being with us for 10 days during pre-season, it's not like he has to learn an entire new system or set-up or anything like that. Even if Egypt makes the final (doubtful), he'd still be back a few days before the start of the season. I know his schedule has been (and will be) packed but he's been off for quite a while now, should be okay.
The reports are conflicting though, some say he made a plea at Liverpool to "let him go", others just say that Egypt is very very eager to have their star player present at the Olympics and he just agreed that he'd go if Liverpool let him. If he's not dead set on participating and just doesn't want to turn down his country, I'd keep him at Liverpool as well. We'll have to miss him for the Africa Cup of Nations as well midway through the season.