I'm agreeing with what D_.. has posted. I'd also add that the expression would have to be either..."My uncle fell asleep at the wheel." which it does not say and in addition that this is a rather idiomatic expression in English which doesn't literally meaning sleeping but that someone, *"is not attentive or alert". He is not doing his job or duties but does not really mean he is driving or in a vehicle.
So, just as D_.. points out we wouldn't use it here.
I would say that (in the UK at least) "... is asleep at the [steering] wheel" is the idiomatic phrase and therefore the obvious translation (I just wrote that). Altho "sleeping at the wheel" is grammatically correct, no one would actually say it.
It is of course true that there is a metaphorical meaning of the expression as jaye16 says, but of course that derives from its common literal usage.
In accordance with so many of your other posts, Bohuslav, you are correct. This exercise is not clear whether it's attempting to translate the English idiomatic phrase (my uncle is not paying attention), OR if it's attempting to say quite literally that my uncle is sleeping (currently) behind the steering wheel of a vehicle.
Based on the limited context given, and considering that the interlocutor survived to recount the story, I would venture to say that the original intention is the former, in which case DL needs to correct the exercise so that the English phrase reads as such:
"My uncle is asleep at the wheel."