Brendan Rodgers has made a bid worth over £30 million for James Tarkowski, the Burnley centre-half.
Leicester have already had one offer turned down for the England international this month and are returning with a second proposal which they hope will persuade Burnley into agreeing a deal.
Rodgers, the Leicester manager, has identified a new centre-back as a priority in this transfer window and Tarkowski, 28, has been a long-term target for the club.
Leicester are operating under a restricted budget but have made a significant offer for Tarkowski, due to the pressing need for defensive reinforcements.
Burnley are demanding the £50m fee written into Tarkowski’s contract yet Leicester are hopeful of striking a compromise due to the severe impact of Covid-19 on football's finances.
It is understood that Tarkowski is interested in pursuing a move to the King Power Stadium.
Leicester have been in talks with Saint-Etienne over a deal for Wesley Fofana but negotiations have stalled due to the rising cost, with West Ham also interested.
Jonny Evans — who returns from suspension this weekend — Caglar Soyuncu and Wes Morgan are the only experienced centre-halves in the Leicester squad and Rodgers had to fill the gap by signing Ryan Bennett on loan from Wolves in January.
Rodgers’s squad has been further decimated with an injury to influential defensive midfielder Wilfred Ndidi, who could miss up to 12 weeks with a groin injury.
Ahead of the visit to Manchester City on Sunday, Rodgers said: "There's a number of players associated with ourselves and it's clear that centre-back is a position where we're looking to bring someone in.
"We'll see what the club can do and we'll take it from there."
Leicester's new signing Cengiz Under, who has joined on a season's loan from Roma, was having his hearing for a work permit on Friday afternoon.
The Turkey international will be unavailable for Sunday's game at the Etihad Stadium.