The rumors were apparently stoked by Apple's announcement at the Worldwide Developers Conference that it has taken steps to make it easier for third parties to integrate the smart home platform into their devices, followed by a comment recently attributed to Nest that it would "consider HomeKit".
At the present time, HomeKit-enabled smart products require a hardware authentication chip to make them compatible with Apple's Made-For-iPhone program. At WWDC, however, Apple said it was updating its specification so that smart products won't have to include a hardware chip and will be able to authenticate through software instead. The news sparked suggestions that some older products could theoretically be upgraded to support HomeKit using a firmware upgrade.
HomeKit has enjoyed fairly wide support among smart gadget manufacturers, but the Google-owned Nest brand has never been on that list. Apple removed Nest products from its stores in 2015 shortly after the first HomeKit-compatible products became available for purchase.
Nest owners needn't completely give up hope for HomeKit support, as manufacturers have occasionally added the standard to products via upgrades well after they have come to market. Add to that Apple's looser licensing and authentication restrictions for HomeKit and it's not impossible that Nest will come around to the platform one day.