No, they're entirely equivalent. See eg https://dictionary.cambridge.org/grammar/british-grammar/near-and-near-to. The difference with close is you /have/ to use 'to' to get this meaning ('the cat sleeps close the dog' is nonsensical)
Yeah, but you know... it is like the native Brazilians who comment here that no one in Brazil ever says, "tu"; English speakers say a wide variety of things in a great many ways. And there's nothing quite like an extended stay in the UK to drive that point home.
I must admit, I have learned almost as much about English as Portuguese since I started studying here.
But, I already knew to never say never. :)