The 22-year-old defender helped the Foxes win promotion from the Championship in 2014, but struggled for first-team selection in the Premier League last season.
He was loaned out to Uwe Rosler's former club Brentford for a second time in February, having made his last league appearance for City in December.
His first loan spell with the Bees was in 2013, when current Leeds head coach Rosler signed him for the Griffin Park side.
According to the Yorkshire Evening Post, Leeds are looking to sign a central defender and Moore is one of their targets if Sol Bamba does not commit himself permanently to the club.
The England Under-21 international has two years remaining on his Leicester contract.