The phrase "a vague connection" is correct and usable in written English.
It can be used when describing a relationship or link between two things that is not clear or well-defined.
Example: "There seems to be a vague connection between the two theories, but further research is needed to clarify their relationship."
Alternatives: "an unclear link" or "a loose association."
Deane added, "I'm not saying it's not possible that there's a vague connection".
He tells the writer that he, too, is from Newark, and reveals a vague connection between his family and Zuckerman's.
Anyone with even a vague connection to the Premier League must be looking forward to the tills ringing.
In the past, the vast majority of Japanese entertainments popular in America — from the sixties cartoon "Speed Racer" to more modern series such as "Final Fantasy" and "Pokémon" — have been set in wildly imaginative worlds with only a vague connection to real-life Japan.
He had only a vague connection with the occupant, who lived there with his partner and her child.
I became curious about this other world, which seemed to have only a vague connection with my scientific training.
I only had a very vague connection with the name Debbie Reynolds".
No monetized environmental performance metrics explains that some ecological services are difficult to monetize because of the vague connection between a service and its ultimate impact on human infrastructure.
He serves up only a cold porridge of archive footage and disconnected soundbites that have some vague connection to the book, without the connecting spine of her explanations.
As a Native American — he is a member of the Cahuilla tribe — he was intrigued by a vague familial connection to Hernando de Soto, the Spanish explorer who enslaved and exterminated indigenous people in his quest for New World riches.
There was a vague family connection to them through my stepbrother Jules.
