The Hammers are currently undergoing somewhat of a rebuild under new boss Julen Lopetegui, who has already spent £65m to sign Max Kilman and Luis Guilherme.
However, there are a number of areas of the pitch that require further strengthening, it well documented that the East Londoners are pushing to bring in Aston Villa forward Jhon Duran.
Furthermore, West Ham's pursuit of a new right-back has been highlighted of late, with Bayern Munich's Noussair Mazraoui known to be on their shortlist.
On Friday afternoon, though, reports in Germany indicated that the proposed deal had broken down and the Morocco international may instead move to Manchester United.
Any developments regarding the future of Aaron Wan-Bissaka - another West Ham target - could play its part in whether that transfer materialises or not.
Williams also on West Ham radar
According to HITC, West Ham are admirers of Forest defender Williams and have been willing to negotiate a deal.
Instead, it is claimed that Forest were quick to reject an offer for the Wales international, the proposal also said to include a West Ham player.
Although the 23-year-old only has a contract at the City Ground until 2026, the report adds that Forest are against a sale at the present time.
Why are Forest insistent on a Williams stay?
Nuno Espirito Santo is not short of competition in that area of the pitch with Ola Aina also an option, albeit the Nigeria international sometimes being required on the left.
Forest also have high hopes for 18-year-old Eric da Silva Moreira, who has been signed from St Pauli, but Williams's own profile is enough to keep him in the East Midlands.
As many as 57 Premier League appearances have been made across the last two seasons, while he carries plenty of attacking pedigree and is versatile down both flanks.
Furthermore, he counts as a homegrown talent. With there being uncertainty over other such players in the Forest ranks, it makes sense for Forest to keep Williams in order to have fewer issues with squad registration.