The Premier League pair have been battling over the 24-year-old's signature.
Aston Villa's Jordan Ayew
The 24-year-old looks set for an instant return to the Premier League as the Mail reports that both clubs have a genuine interest in his signature.
However, the Mail claims that sources close to the player believe that he is destined to move to the London Stadium, where he would link up with older brother Andre who also appears to be on the verge of joining the Hammers after a £20m fee was agreed with current club Swansea City.
Andre Ayew looks set to complete a switch to West Ham
Though the Baggies will undoubtedly be disappointed to miss out on the Villa man, the Mail suggests that both players joining the Irons is likely to leave the path clear for Tony Pulis to make a move for another striker target, Enner Valencia.
The 26-year-old - who has found life in the Premier League difficult, it seems - would surely struggle for opportunities if he had two more rivals in his position, and it seems unlikely that with West Brom's move for Diafra Sakho falling through at the last minute (via Mail), that Bilic will have too many problems letting the Ecuadoran move.
And with Pulis boosting few options up front, the lure of first-team football may be enough to tempt Valencia to complete the switch to the Hawthorns.
But it remains to be seen if potentially landing Valencia would be any consolation if they do ultimately miss out on signing Jordan Ayew.
West Bromwich Albion manager Tony Pulis could turn his attention to Enner Valencia if Jordan Ayew follows his brother