Godfrey has been watched several times by Tottenham this season, while Arsenal are also said to be keen.
Norwich value their star centre-back at £50 million, but Spurs and Arsenal are both reportedly hopeful of getting a deal done in the summer.
Norwich look set to face the drop this term, which means that they may be forced into some sales.
Tottenham and Arsenal are now both said to be prepared to battle to sign Godfrey, who is believed to have a very bright future.
The youngster has shown some weaknesses, but his composure in possession and speed across the ground means that his potential is obvious.
Spurs and Arsenal have both struggled at the back this term, with their defences not exactly rock solid.
And it could be that Godfrey is lined up as a long-term solution for both the North London sides.
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