Following the 'Baggies' relegation to the Championship, Evans has a release clause of just £3million, attracting a host of interest from numerous Premier League clubs.
Leicester are reportedly the frontrunners to secure the centre-back's signature but are not happy with the potential £4million added cost in agency fees.
The amount would be greater than the transfer itself and has led to serious discussions among the club's hierarchy.
However, if they can come to an agreement, Leicester would be acquiring a defender with tonnes of experience, who could replace the departing Robert Huth and make a great partner for Harry Maguire.
Evans spent nine seasons at Manchester United before moving to West Brom in 2015, making 95 appearances for the relegated club across three years.