When Manchester United paid Leicester City £80million for centre-back Harry Maguire in August, the Foxes did not replace the England international.
Fresh after going second in the Premier League after thrashing Southampton 9-0 on Friday night, manager Brendan Rodgers confirmed the club's desire to recruit a new defender.
"We're looking at all options to see if we can strengthen in January. It's always a difficult window. You'll always look and if there's value there, then we will do something.
"I've always tried to be positive in the January window. It's normally worked fairly well for us when the availability has been there.
"[At centre-back], it's one where we're planning forward, if you look at Wes [Morgan] and where he's at in his career."
One such option could be Celtic's £20m-rated Norwegian Kristoffer Ajer, report the Daily Mail.
Leicester had a scout at Parkhead on Thursday as Neil Lennon's men came from behind to beat Lazio with the centre-back in commanding form.
Ajer was linked with a move in the summer and has been talked up as the next Celtic player to leave for huge money.
The Parkhead side would likely be reluctant to sell in January due to the club's demands on three fronts (Betfred Cup finishing before then), including a tight title race with rivals Rangers as they pursue nine-in-a-row.
However, the Foxes could make Filip Benkovic part of the deal.
The centre-back excelled during a loan spell in Glasgow last season and has not been involved with the first-team at Leicester, playing four times in Premier League 2.