Leicester are expected to make a move for Bayer Leverkusen defender Jonathan Tah if they cannot agree a deal for Burnley’s James Tarkowski.
As Sportsmail reported in August, the Clarets are still demanding £50million for the centre-back, with Leicester offering an in excess of £30m on Friday, which was subsequently turned down.
West Ham failed with a series of bids for Tarkowski while Leicester have been similarly frustrated in their move for St Etienne defender Wesley Fofana.
Former Foxes boss Claude Puel is now in charge of the Ligue 1 side and is reluctant to let Fofana, 19, go despite offers around the £30m mark from Leicester and the Hammers.
Tah is a Germany international who developed into a key man for Leverkusen since moving from Hamburg five years ago.
The 24-year-old is well known by Leicester head of recruitment Lee Congerton, who worked at Hamburg from 2011-14.
Meanwhile, Rodgers revealed he is chasing three more signings before the window closes on October 5 after detailing his plans to the board over the summer.