idioms - Expression for indirectly asking someone to do something

Could there be an English expression (a verb or an idiom) for indirectly asking someone to do something that you want them to do that you find it awkward to ask them to do?

For example, let's say you're in a restaurant. And the seats are full and your waiter wants you to eat your meal faster and make your seat available for other customers, because you're there like a couple of hours.

The waiter doesn't have the stomach to ask you to finish your meal already, so he is asking you whether you're done with your meal, in an effort to hint that he wants you to finish your meal ASAP.

Is there a single verb or an idiom describing the waiter's action in this type of situation?

For example, could there be a verb or an idiom that fits in with this sentence?

The waiter ____________ that he wants you to finish your meal ASAP.

I was thinking along the lines of the verb 'hint' or 'insinuate', but I was wondering if there could be verbs/idioms that are more fitting in this kind of situation.