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The two clubs have reached agreement on a fee, believed to be in the region of £200,000 plus 50% of any future transfer fee, and all that now remains is for Green to agree personal terms.
The 21-year-old told the Hull Daily Mail: "I know there have been a few developments over the past few days and the two clubs have agreed a fee, which is great.
"To be honest, I just tried to put everything to the back of my mind on Saturday and just concentrate on playing against Bournemouth.
"The plan is to get something sorted out early this week. I'll be talking to the chairman and if we can agree everything, then I'd be happy to sign.
"It's just a matter of personal terms. I've always said this is the place I would like to be. Now the fee has been agreed let's see what we can do."
Green is regarded as one of the brightest prospects to come through Newcastle’s academy in recent years but failed to make the breakthrough into the first team because of the competition for places.
However he has proved himself in the third division this season, scoring five times in twenty games.