Fulham made one attempt to sign the 20-year-old earlier in the January transfer window as head coach Rene Meulensteen looks to strengthen a backline that has conceded 48 goals in 22 Premier League matches this season.
Moore has previously had loan spells with Brentford and Bradford but has established himself in Nigel Pearson's plans this season, featuring in 23 of the Foxes' 26 Sky Bet Championship games this campaign.
Fulham have been persistent in their pursuit of Moore but Leicester are holding firm in their insistence they will not sell Moore as they try to secure promotion to the top flight.
The two teams could conceivably swap divisions next season, with Leicester top of the Championship table going into the weekend's fixtures.
In contrast, Fulham sit 17th in the Premier League, just one point and one place above the relegation zone.