The report states that the Baggies have already had one bid turned down by the Reds, but they are ready to make an improved offer to land the former Sheffield Wednesday man who has emerged as one of their top targets in the January transfer window.
Tony Pulis has been given funds to strengthen his squad and the need to sign a winger was something that he commented on to the Birmingham Mail in midweek.
Antonio has been in fine form for Forest since arriving at the City Ground this summer and he would be a major loss to their starting line-up, but the lure of the Premier League may convince him to depart - should the Reds receive an offer they feel it is acceptable.
Antonio has scored 10 times in 30 games for Forest this term, with his bludgeoning style threatening defences across the Championship.
The problem for Forest is that finding a replacement of Antonio's quality, if they do allow him to leave, would be a very tough ask.
Stuart Pearce's side are currently under a transfer embargo and they would only be able to look towards the loan market or the free transfer list to bring somebody in.