An eighth season of the CW drama will debut in the US on October 3.
"I can tell you there is no talk about cancelling it," Carver told Assignment X.
"The storylines we have set up for this year set up the show for years to come. So we are certainly not thinking of ending it any time soon."
Carver also expressed his hopes that Supernatural will be given sufficient time to wrap up its storylines once the show does come to an end.
"It would be a shame if there was not a set ending for the show," he admitted.
Supernatural exec Robert Singer recently hinted that season eight will be closer in tone to the show's early episodes and "a little less earnest" than recent years.
Supernatural airs on The CW in the US, while Sky Living have broadcast rights in the UK.
> Jared Padalecki hints at Supernatural season eight twists
Watch a clip from season seven of Supernatural below: