Following their recent relegation from the Premier League, the 30-year-old has a release clause in his deal with the Baggies that allows him to leave for under half of the £7m paid by the club when they signed Evans from Manchester United in 2015.
Should the Foxes sign Evans, it would represent a real coup for Claude Puel's side, as the player was linked with moves to the likes of Arsenal and Manchester City in January for £25m, while he boasts a wealth of experience.
Making 235 Premier League appearances during his career, 28 of which coming for West Brom last season, Evans also owns three Premier League and one Champions League winner's medals from his time at Old Trafford, and has 69 caps for Northern Ireland, four of which came during their Euro 2016 campaign.
With Puel already signing FC Porto full back Ricardo Pereira, the addition of an experienced campaigner such as Evans will help sure up a defence that conceded 60 Premier League goals last season, with only four sides conceding more.
Despite news of a potentially shrewd incoming at the King Power Stadium, one man who is expected to leave the club this summer is Riyad Mahrez, as reports claim that Manchester City are close to signing the Algerian international for fee of £75m.