Minish Cap has your standard references and call backs to other LoZ games without any direct connections... so in that respect Minish Cap is as "connected" to the rest of the series as any Zelda game is that doesn't make any clear direct connection to another game in the series.
For instance, Ocarina of Time is clearly connected to Majora's Mask since it's the same characters (Link, Zelda, Skull Kid, Mask Salesman) and Twilight Princess (Skull Kid again, Temple of Time, Hero's Shade) and even A Link to the Past due to Ocarina being a depiction of the Imprisoning War. Zelda II is a direct sequel to the first LoZ. PH and ST are sequels to Wind Waker which is itself only loosely related to Ocarina by vague references to the Hero of Time and direct references to the sages from Ocarina.
But there are no clear connections between the Oracle games & Link's Awakening and the rest of the series. Nor is there any connection between the first two games the rest of the series. It's easy for me to brush off SS because it has tenuous connections to the rest of the series.
But the theory of Minish Cap being close in proximity to Ocarina of Time is a decent one based on the games having the same characters. However, the NPCs that debuted in Ocarina are only duplicated in Majora's Mask because Termina is a parallel world to Hyrule. So why would the same characters be in Minish Cap? They're all the same age, and Dampe is alive which would suggest that if Minish Cap is closely relative to Ocarina it would be taking place during Link's childhood. Perhaps the characters in Minish Cap are all descendants of Ocarina of Time's denizens and bear the same names. But keep in mind that the character Anju from the Minish Cap bears the name of the lady who runs the Stock Pot Inn from Majora's Mask, whereas in Ocarina she has no given name and is just unofficially known as "The Cucco Lady." Maybe the two share the same name regardless...
One major inconsistency is that Minish uses Wind Waker's aesthetic style. Minish Cap's Zelda could be Ocarina's Zelda given that Minish Zelda uses the look for Wind Waker's chibi Zelda whose appearance was based of Adult Zelda from Ocarina, but young Zelda doesn't dress like that in Ocarina of Time. Perhaps she's a slightly older child Zelda who is starting to adopt the royal garb she wears as an adult?
Minish Cap's Hyrule is also clearly different than Hyrule from Link's childhood in Ocarina of Time. It could perhaps take place in a different region of Hyrule from Ocarina of Time and the characters settled there? It's a stretch.
Minish Cap's Hyrule could also just be a parallel dimension Hyrule even if that's never explicitly stated.
