A fifth series of the sci-fi drama will debut on ITV1 on Saturday (June 16), a year after the episodes aired on digital channel Watch.
On the prospect of a sixth run, Spearritt told TV Choice: "There's been no mention of it to me. It's a difficult one. We've had five series and it would be lovely if it did carry on. [But] it's kind of tough though because I hope it hasn't lost momentum.
"If we made another one, by the time it's shown again, all the fans will have been waiting a couple of years and I don't know if that's entirely fair."
A new Primeval spinoff - subtitled New World - was officially announced in February 2012.
"I'm excited about seeing [the spinoff show], and it's nice that the concept carries on," said Spearritt. "I'm just intrigued really to see how they do it."
The "older, darker and scarier" series has filmed in Vancouver and will be broadcast on Watch in late 2012.
"It'll be interesting to see what they do with the locations," she added. "I suppose it will be strange, but I'm excited for it as well."
It is currently unclear if ITV will transmit Primeval: New World.
> Primeval Q&A: Series five preview
Watch a clip from the fifth series of Primeval below: