Jennifer Lopez & Casper -- Legal Threats Over 'Gay Sex Club' Reports

Jennifer Lopez and Casper Smart are FURIOUS over reports Casper was "caught" in a "gay sex club" and an exotic massage parlor ... and now they're threatening to sue ... claiming the stories are pure BS.

TMZ has learned ... the couple's high-powered attorneys, Shawn Holley and Howard Weitzman, have teamed up and fired off letters to Star Magazine and In Touch ... warning them the "reports" are "false, malicious and defamatory" and will cause "immense damage" to the couple's careers and reputations.

The reports include photographs of Casper outside a XXX peep show in NYC back in July -- Star claims the shop is a "well-known cruising spot for gay men looking for instant hookups."

In Touch claims Casper was "caught" with an "exotic masseuse."

In their letters, the lawyers have each demanded the mags print a full retraction ... warning Smart and Lopez will "immediately file a lawsuit" if the magazines fail to do so.