"I don't dislike anybody enough to train for those 10 weeks and give it my all apart from Liam.
"The offer still stands, I'm available, let's do it for the NHS."
The 46-year-old star branded Gallagher an "archetypal schoolboy bully" and admitted he puts all his frustrations with other people onto the Once hitmaker.
He added: "Anybody that's ever bullied me at all, I forget about them and put it all on to one person and that's Liam.
"And that's why I want to fight him in the ring."
Last October, Williams - who first laid down the gauntlet to Gallagher at the 2000 Brit Awards with a £100,000 ($199,000) bet - suggested the pair go head-to-head in a "professional" boxing match, but retracted the following month when his wife Ayda Field called the idea "embarrassing".
"You are 45, man," Field said. "You're going to go in a ring and smack each other? It's just lame.
"First of all, neither one of you are at your top, peak form. You are not in your 20s, I hate to break it to you. You are both peppered at this point. Your back's going to go out, your knees are going to buckle. I am going to have to bring you back from the dead after this. I don't understand it.
"I am going to knock the hate out, so you feel no need, to the point where you might even send Liam Gallagher a Christmas card. We're going to melt the ice off that snowman."
Williams eventually agreed with his wife, and said he would instead try to bring some "joy" to the Shockwave singer, especially with Christmas approaching at the time.
He said: "This is the festive season of giving and joy to all men, even Liam Gallagher. Thank God we have steered this tanker around to where we should be."
