"I want to fight Conor," Tyron said on "The Hollywood Beatdown."

"I'll fight him in Ireland. I'll fight him in the f*cking back alley of a White Castle ... want to go to Russia? Want to go to the TMZ newsroom?"

"Quit being a bitch ... let's fight."

So, why would Conor take that fight?

Woodley points out that both guys are coming off losses in world title fights -- and since they're close in weight, it makes sense for them to battle while they wait for their shot to get their belts back.

Of course, Conor has said he wants fights with Nate Diaz and Cowboy Cerrone in addition to a rematch with Khabib Nurmagomedov ... but Tyron says none of those fights are happening any time soon.

"Looks like we dangling around Conor ... come get this smoke."

Woodley's last fight was 3 weeks ago when he lost the welterweight belt to Kamaru Usman, who seems to be on a collision course to fight Colby Covington next.

Tyron says it doesn't make sense to refight other contenders he already washed in the welterweight division ... so Conor is the next best thing to a rematch with Usman.

In fact, Tyron says he's healthy and hungry and ready to fight right now ... as long as Dana White can get Conor to sign a contract.

Tyron and Conor have had beef before -- when they got into an altercation behind-the-scenes at the UFC 205 press conference back in 2016.