The Dutchman is out of the season following an ACL injury, while Paul Dummett also faces surgery on a tendon injury.
Newcastle wanted Rose during the summer, but a move didn’t work out and Willems was signed on loan instead.
The 29-year-old is currently out of favour at Tottenham and will be allowed to leave if the right offer comes in with less than 18 months left on his contract.
Newcastle could do with the services of a player that has 29 England caps under his belt and twice made the PFA Team of the Year.
Rose has started just one league game since Jose Mourinho arrived at Tottenham, and the Portuguese has preferred to play centre-back duo Jan Vertonghen and Japhet Tanganga in the position recently, while Ben Davies and Ryan Sessegnon are also ahead of him in the pecking order.
With Euros 2020 on the horizon, the Spurs star needs to play regularly to have a chance of making Gareth Southgate’s Three Lions squad, and a move to Newcastle could do him a lot of good as he will be an automatic starter under Bruce.