Williams was a top target for Southampton but they were unwilling to pay the £2m loan fee that Manchester United were demanding.
The Saints eventually signed Chelsea right-back Tino Livramento on a permanent £5m transfer instead of paying a big loan fee for the Manchester United star.
Norwich have emerged as a potential destination for Williams and he is believed to be keen on the move as well.
The newly-promoted Premier League side have held talks with Manchester United over taking the defender to Carrow Road on loan.
But the two sides are yet to discuss the contentious loan fee, which stopped Williams’ move to Southampton.
It has been claimed that the Canaries would like to pay a similar amount to that which they paid to Chelsea for Billy Gilmour’s loan.
Manchester United are yet to finalise whether to loan out Williams as they want to wait and watch how Alex Telles recovers from his injury.
Ole Gunnar Solskjaer is worried that the Brazilian could be out beyond the end of the transfer window.
