Dave Portnoy claims he was recently offered a role in Washington D.C. -- but had he accepted, he would've had to hand over the reins to his Barstool Sports empire.

El Pres dropped the news on his "Davey Day Trader Global" show on Tuesday ... revealing the position would have been in the Department of Commerce under Secretary Howard Lutnick.

Portnoy explained he got a phone call gauging his interest in the opportunity a few months ago ... but it was made crystal clear he'd have to give up his role with Barstool in order to make the move.

Pres didn't reveal whether he was flirting with the idea ... but said even if he was, they never followed up -- which he called "weird."

The topic came up over his confusion with Elon Musk's involvement with the Department of Government Efficiency ... all while the tech billionaire still operates Tesla.

Regardless, it likely would have been hard for Portnoy to take a step back with Barstool -- after all, he did turn it from a silly gambling newspaper into a massively popular company.

Portnoy is a big supporter of President Donald Trump, though ... so the offer had to have at least been appealing.