Newcastle United have reportedly upped their bid to £24 million pounds for star striker Saido Berahino
Albion have already rejected £21 million bids from Newcastle United and Stoke City earlier in the day.
Reports also indicate Stoke City are currently in advanced talks with the striker, but these claims have been dismissed.
Newcastle's initial bid was believed to be £21m cash upfront.
Tottenham and Chelsea are also continuing to monitor the situation.
The Express & Star reported on Friday that Tony Pulis's side would not be selling last season's top scorer to relegation-threatened Newcastle - who are just seven points behind the Baggies.
There is also reported interest from title-chasers Tottenham Hotspur, and Albion - despite publicly saying the 22-year-old is not for sale - would listen to offers of more than £20 million, as long as they are not from Newcastle.
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Berahino made a timely return to the starting XI on Saturday, netting twice as the Baggies were held to a 2-2 draw by Peterborough in the FA Cup.
And chairman Jeremy Peace does not want to risk strengthening a rival in the bottom half of the table with Premier League survival - and next year's multi-million-pound new television deal - at stake.