West Bromwich Albion and Newcastle have been credited with an interest in the 91-cap international.
The Inter Milan left-back will only have 18 months to go on his existing deal come January and a host of Premier League clubs are seemingly interested in him.
But it seems unlikely that West Brom will be among them when the transfer window re-opens.
Gibbs, previously called "outstanding" by Baggies boss Tony Pulis, has done nothing to suggest that Pulis will be interested in bolstering his options in that role.
The ex-Gunner did have a plethora of injury problems once upon a time but he seems to have put them behind him.
Nagtomo won't be cheap, considering his profile and the fact he has 91 caps for Japan, and it seems pointless for him to sit on the bench in the West Midlands.