The England Under-21 star may be available at the King Power Stadium if Nigel Pearson manages to sign Gareth McAuley.
There is a transfer chase going on that could net Leeds one of the top young central defenders in the country, according to reports in the Yorkshire Post.
Leicester's pursuit of McAuley is peculiar on one level considering they have someone as promising as Moore in their ranks.
The England Under-21 star, currently with Gareth Southgate's side as they prefer for the European Championships in Czech Republic, made just 14 appearances for the Foxes last season, though he started the club's first nine league matches of the season.
Moore was a central part of Leicester's promotion campaign in the 2013-14 season, where he played 30 times to help Nigel Pearson's men win the Championship, so if he was to come in at Leeds, albeit it on loan, the 22-year-old would have recent experience of what it took to help a side into the Premier League.
With continuing reports that the Whites are looking for central defensive enforcements, those at Elland Road may well consider hanging tight to see what happens at the King Power Stadium, because if Moore becomes available, he would make an outstanding defensive signing for Uwe Rosler's side, having previously been on loan under the German at Brentford.