The 21-year-old agreed to come to Hull on a season-long loan from Newcastle, but the Toon have received several transfer bids for him.
However, Green says he wants to stay with City for the rest of the season, and then look at his options.
Tigers boss Jan Molby said: "It's a difficult situation, but I spoke to Stuart yesterday and he told me he wants to stay with us and see out the rest of the loan agreement.
"He said he's enjoying his time with us and he's not really interested in a permanent move elsewhere.
"He wants to play for Hull for the rest of the season - and then consider all the options."
Meanwhile Molby says that it's unlikely anyone will be signed ahead of Saturday's game at home to Bury.
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