The defender had looked set to move to the Hawthorns after the Baggies agreed an £8 million move with the Tigers earlier on Tuesday, say the Yorkshire Post, but the former Manchester United man is now at the centre of a tug of war between the two Premier League clubs, both of whom are offering him an immediate return to top tier football after Hull were relegated in May.
The 26-year-old has been a key figure at the KC Stadium since joining five years ago, making 172 appearances for the Yorkshire club.
The Yorkshire Post report that Chester had been given permission to head back to the UK from Hull's training camp in Austria to discuss a transfer to the Hawthorns, and he may now end up heading to Leicester as well to look into an alternative move.
Central defenders have been much in demand this summer in the Premier League, and the Wales international is just one of a series of players that have been courted by more than one club after the transfers of Toby Alderweireld to Tottenham and Angelo Ogbonna to West Ham.
Leicester have already signed defenders Christian Fuchs and Robert Huth this summer, while West Brom have only brought in James McClean, and have seen several first team players depart the club.
With the Foxes eager to strengthen in Claudio Ranieri's first season at the club, there are cases to be made for either side needing defensive additions the most.