The report claims that Leicester boss Claudio Ranieri is a fan of the young defender, and Burke is keen to move to the East Midlands in order to have a shot at Champions League football.
Capable of playing at either centre-back or on the right of defence, Burke came through the West Ham youth teams and made his debut during a 5-0 defeat to Nottingham Forest in the FA Cup.
The England U20 international has a big future ahead of him, yet his future may lie away from East London if reports of Leicester’s strong interest are to be believed.
The Foxes currently top the Premier League table and even if an unthinkable title triumph slips away from them, the club are all-but guaranteed to feature in next season’s edition of the Champions League.
The Sun highlights European football as a key factor in Burke’s interest in joining Leicester, though with West Ham still capable of grabbing fourth spot, perhaps there is another motive behind the speculation.
Burke would provide decent cover for Leicester’s back four and is impressive with the ball at his feet.