Sources with direct knowledge tell TMZ ... the Bravo personality and Tom Hanks' son did NOT hook up during their time in the 'The Surreal Life' house -- though some people in the cast did feel the pair had sexual chemistry.

Still, we're told nothing physical occurred between Kim and Chet ... even though MTV's first look for "Surreal Life: Villa of Secrets" showed the 2 contestants embracing in a bedroom with the lights off.

As TMZ previously reported ... Kim and Chet had a flirty relationship while in Colombia for the show's production. They even exchanged digits before going their separate ways.

Sources confirm KZ and CH do have each other's contact info ... but they aren't in regular communication. In fact, their connection isn't as serious as it's been made out to be.

We're told Kim isn't focusing on dating amid her messy divorce from Kroy Biermann -- with whom she separated last year after almost 12 years of marriage. Remember, Kim and Kroy have been battling it out in court over a number of issues ... including child custody and finances.

Kim's got bigger fish to fry right now ... namely, trying to sort out her financial woes and getting their house sold before the bank forecloses. So, it's no wonder dating isn't on her mind these days.