Andy Cohen's not leaving Bravo despite reports claiming he's negotiating a departure package amid legal troubles -- with a network rep blasting the unsubstantiated rumors.

A spokesperson for Bravo tells TMZ ... there is absolutely no truth to the rumor Andy's negotiating an exit from the network -- and they're shutting down any such notion as patently false.

Sources with direct knowledge also tell us a report that cited an anonymous source to run their headline was way off base, and that none of the info that got published was accurate.

The report in question alleged that he was leaving Bravo as a result of the mounting allegations he's been hit with of late in different lawsuits -- including claims brought by former 'Housewives' stars Brandi Glanville and Leah McSweeney.

Remember ... Glanville's lawyers sent a demand letter to NBC back in February -- claiming she'd been used by producers over the years and put the network, and Andy, on notice.

McSweeney, meanwhile, claimed Bravo created a toxic work environment and preyed on her alcohol abuse issues for ratings -- and claimed Andy used cocaine with 'Housewives' and other Bravo stars, allegedly rewarding those who participated in such exploits.

Of course, Andy denied those allegations ... and Bravo's fighting those lawsuits.