Smith, who is one of four boxing brothers, has signed to fight on Sky Sports with promotional stable BOXXER.
That means that he could be given the chance to fight Eubank Jr, which he says he would not hesitate to accept straight away if it were offered to him at this moment in time.
Speaking to Sky Sports, he said: “I’ve always put my name in for that.
“That’s a fight that I’d jump at tomorrow. That’s a fight that I’d love, that’s a fight that I know could be made now. With me back on Sky that’s one that they’ll probably push to make.
“If Chris Eubank fights me the way he fought Liam Williams, I think I’d beat him handily.
“I think he’s stuck in styles, trying to fight the way Roy Jones fights. So that’s one that I’d bite your hand off for and I’d bite your hand off for it next, if you want the truth.
“We had some good spars and you can’t really take too much off a spar, sparring in general. But them spars, we done a lot, have also made me massively confident I’d beat Chris Eubank.
“If he comes for a fight, you’re in for a fight with him; he’s a good athlete, fit. He’s not strong but he’s fit.
“Boxing ability and boxing IQ I don’t think he’s the greatest. That’s why I think he’s stuck in between styles at the moment. I think Roy Jones is trying to get him boxing and if he tries to box me like he boxed Liam Williams, then I think it’s an easy night for me.”
As well as Eubank Jr, Smith also fancies a crack at Jermell Charlo and Tim Tszyu.
He added: “It’s exciting the position I’m in at the moment.
“If all four belts become vacant, I’ll probably get a choice of route.
“The British fans know me. Put a fight in front of me, I’ll take it and I’ve done that the whole way through my career, whether it be Russia, whether it be drop back down a level for a domestic fight with Anthony Fowler.
“Offer me a fight, I’ll take it. I like a fight.”