The Foxes have already made one move in the transfer window this month, snapping up winger Demarai Gray from Birmingham City as Claudio Ranieri makes calculated additions to his squad.
With question marks over the future of summer signing Yohan Benalouane, Ranieri may be looking to bring in another versatile defender - and he could raid a Premier League rival.
The Daily Mail report that Leicester are weighing up a move for West Brom defender James Chester, who helped Wales win qualification to this summer's European Championships in France.
Chester, 26, signed for West Brom from Hull City during the summer, but has made just one Premier League start for the Baggies, so the defender may want first-team football ahead of Euro 2016.
It's stated that, given Chester's lack of football at The Hawthorns, Baggies boss Tony Pulis is open to a deal this month, with Leicester plotting a move.
The report suggest that, having been priced out of a move for Dynamo Kiev defender Aleksandar Dragovic, Leicester will now pursue a deal for Chester, whose versatility to play at centre back as well as full back is appealing to Foxes boss Ranieri.