Williams has 18 months left on his current deal and talks over a new contract have failed to find an agreement.
A host of clubs, including the likes of Aston Villa, Newcastle and Bolton, have been linked with Australian star Williams in recent weeks and now West Brom are believed to be keeping close tabs on his situation.
But with Boro firmly embroiled in a promotion bid, Williams is believed to be more than happy to remain at The Riverside until the summer at least.
Boro are also now in a position where they do not need to cash in on their prized assets and would fend off any bid for Williams.
Sky Sports claim West Brom would have considered an exchange deal after Boro showed an interest in their striker Simon Cox.
However, should Boro pursue Cox, it appears unlikely Williams would be heading in the opposite direction.