LeBron James and Stephen A. Smith can end their feud once and for all with their FISTS ... 'cause TMZ Sports has learned a popular boxing promotion is drafting an offer to make a fight happen!!

King James and the ESPN talent have exchanged verbal blows ever since their infamous confrontation at the Lakers game earlier this month ... and on Wednesday, the argument turned to hypothetical violence -- with SAS claiming if LeBron put his hands on him, he would've retaliated with a punch.

After LeBron trolled the hell outta Smith by posting his old training vids, Celebrity Boxing founder Damon Feldman immediately got to work ... and started making calls to rich investors in hopes of putting together the funds needed to lock down a matchup of this caliber.

AKA -- he hit up his contacts in Saudi Arabia.

Of course, neither James nor Smith needs the money ... as the two are among the highest-earning figures in their respective fields.

But don't scoff at the idea just yet -- it's clear they can't stand each other at this point

There is one big problem, though ... as Smith admitted he'd get his ass kicked by James in a bout -- so chances are he's too proud to let the internet witness that and let it live on social media forever.