Yes and no. A British channel has commissioned a show called "Meet the Markles", but it's no Keeping Up With the Kardashians, despite the misleading sounding name.
Channel 4 is reportedly hard at work on what sounds like a quasi-documentary about the actress (who alas they seem to be mostly interested in as an accessory to Prince Harry). It will reportedly include interviews with people who know Meghan, and will also get into how she and Harry met.
The real focus, however, seems to be digging up "dirt" from Markle's past (if it exists), both recent—her marriage that ended in 2013—and a look at her family ancestry.