Reports indicate that the former Premier League champions have already made a bid of £2.5m for Marseille player Bouna Sarr, who can play as either a right-back or a winger.
That bid looks set to be rejected by the French club, but the 'Foxes' will allegedly return with a revised offer.
The 25-year-old has made 51 appearances for the Ligue 1 side, scoring twice, since joining from Metz in 2015.
Leicester have already been active this January, signing young forward Fousseni Diabate from Ligue 2 side Ajaccio in a £4.4m deal.