The Senegalese forward is also reportedly being chased by former club West Ham.
Former Chelsea, Newcastle and West Ham striker Demba Ba is being heavily linked with a switch back to the Premier League this summer, and West Brom are eager to steal in front of his other suitors by offering the 30-year-old the highest wages in their history, according to the Express and Star.
On top of that, they may well be prepared to break their transfer record in order to match the £10 million bid Shanghai Shenhua have already made for the Besiktas striker.
It remains to be seen whether Bilic would agree to impact his transfer budget and wage budget for the player, but it is clear a forward is on their list of priorities considering Charlie Austin is also being pursued.
Is Demba Ba worth it?
Well, the forward had a fairly nomadic career in England, taking in three different clubs in five seasons, but he managed to find the net regularly, even scoring key goals when occupying a bit part role at Stamford Bridge.
43 league goals in 93 league matches is a very good ratio for any side looking to stregthen their attacking areas, and Ba followed that up with an outstanding season in Turkey where he scored 27 goals for Besiktas - his highest ever total in a single campaign and proof that he can be formidable if he is given the right service and regular playtime.
With the Baggies having to rely on Saido Berahino for large portions of last season, Ba would certainly be another quality addition up top, as doubts remain over the future of Victor Anichebe and Brown Ideye.