The Tigers are on the look out for another striker as they battle to beat the drop and Gestede has been mentioned as a possible target when the transfer window re-opens.
The former Blackburn forward has managed four goals in 13 Championship outings this season and reports in the press claim he has also caught the eye of the Baggies.
Albion boss Tony Pulis is also eager to add to his options up front amid doubts over Hal Robson Kanu, who has made all eight of his Premier League appearances from the bench this season, and Saido Berahino.
Berahino, 23, has managed just four league appearances this season and continues to be linked with Stoke City.
Gestede is under contract with Villa until 2020 but could be open to a move to the Hawthorns due to the lure of Premier League football and the fact he could stay in the Midlands.
However Villa are keen on Tigers striker Abel Hernandez and that could swing the deal the way of Mike Phelan’s men if a swap deal could be arranged.
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.