The women of the new "Baywatch" reboot may be bringing the heat on camera ... but behind the scenes, there's competition brewing over who's becoming the franchise's next breakout bombshell.

A source on set tells TMZ ... there's some "tension" over who's filling the Pamela Anderson lane in the modern version of the iconic series ... and the contenders are Brooks Nader and Livvy Dunne.

Brooks certainly has the edge when it comes to screen time ... because she appears in virtually every episode ... while Livvy is only featured in three episodes -- less than half the season.

That said ... Livvy's massive social media following still gives her major star power offscreen ... something that hasn’t gone unnoticed during filming.

We're told the rivalry talk became a recurring topic behind the scenes ... with both women openly discussing the "next Pam Anderson" comparison at different points during production.

As one source put it ... "There's been some tension between the two” ... with Brooks especially laser-focused on making the reboot her show.

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And based on a recent red carpet appearance for Sports Illustrated Swimsuit, Brooks seemed especially aware of how the cameras were capturing Livvy -- even telling photographers to get her good side while the two posed together.

In other words ... the slow-motion running scenes may not be the only thing competitive on set.