Here's the deal ... The Hollywood Reporter gave fans of 'TDS' an inside look at how Jon Stewart's return to Comedy Central's flagship satirical news show came to fruition -- and Minhaj got name-dropped in the piece.

Basically, THR says the deal was right at the finish line, just needing to cross the t's and dot the i's over the summer to bring HM on as Trevor Noah's replacement ... until the New Yorker published their exposé on Hasan embellishing stories in his stand-up special.

Remember, the magazine alleged Hasan hammed up stories for the shock value ... including one about taking his daughter to the hospital because of an anthrax scare and another where he said he was turned down by a girl he asked out because of his race -- something the woman in question flat-out denied BTW.

Minhaj -- who appeared as a guest host in the year-plus since Noah went off the air -- has defended himself, denying some of the New Yorker's assertions ... but THR says the scandal was "suddenly seen as a liability" so higher-ups backed off hiring him.

The backlash to Hasan's scandal was swift ... with some comedians frustrated over Minhaj saying they all embellish with their stand-ups. Bill Maher straight-up called the guy a liar on an episode of his show back in October.

As we previously reported ... producers recently announced a tried and true part-time option -- bringing back Jon Stewart to host the show on Mondays through election season and executive produce the show through at least 2025. Hosting duties from Tuesday to Thursday will be handled by correspondents on a rotating basis.