Baggies boss Tony Pulis has other defensive targets including Manchester United pair Chris Smalling and Phil Jone
West Brom are preparing a third bid for Middlesbrough defender Ben Gibson.
MirrorSport understands the Baggies have had two offers rejected.
But the Premier League club are not giving up after relegated Boro told Gibson he can go if they get a big offer.
Now Albion are considering bidding a club-record £20million for Gibson, who has 10 England Under-21 caps.
Gibson, 24, is also on the radar of Tottenham and Leicester.
Baggies boss Tony Pulis has other defensive targets including Manchester United pair Chris Smalling and Phil Jones.
The duo could potentially leave Old Trafford this summer following the arrival of Victor Lindelof.
Smalling, 27, and Jones, 25, both have two years left on their contracts.
Pulis is monitoring them as he knows Albion are still at risk of losing stopper Jonny Evans to Leicester.
Pulis has so far only brought in striker Jay Rodriguez from Southampton for £12million and Egyptian defender Ahmed Hegazi on loan.
A permanent deal for Bournemouth defender Marc Wilson, who spent the second half of the season on loan at the The Hawthorns, remains likely.
But Pulis is prioritising other signings first who will go straight into his starting line-up as Jonas Olsson left and Gareth McAuley is 38 in December.