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.
Gareth Bale could leave Real Madrid this summer despite proving to be the match-winner during Saturday's Champions League final.
Brighton are stepping up their recruitment drive this summer with Reading defender Liam Moore next on their list of targets.
Everton are in the hunt to sign Chelsea striker Michy Batshuayi but he will not make a decision until after the World Cup.
Manchester City goalkeeper Joe Hart has emerged as a shock transfer target for arch rivals Manchester United this summer.
Chelsea are showing an interest in Napoli full-back Elseid Hysaj, who could join Maurizio Sarri at Stamford Bridge, reports claim.
Arsenal are reported to be locked in talks with Switzerland right-back Stephan Lichtsteiner, who is set to leave Juventus.
Gareth Bale has suggested he could be on the move following his Champions League heroics, with Manchester United in the hunt.