Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
Clifford, released by the FA Cup holders in January, has been training with the Foxes' development squad and the midfielder scored the winning goal for Steve Beaglehole's Under-21 side in a 2-1 victory over Birmingham last month.
Dublin-born Clifford, 21, is described by Leicester as a tough-tackling central midfield player with an eye for goal.
He was called into Giovanni Trapattoni's Republic of Ireland squad for their World Cup Qualifier against Germany in October 2012, but the player has yet to make a senior appearance for his country.
Clifford joined Chelsea in 2007, winning the FA Youth Cup with the Blues three years later.
During his time at Stamford Bridge he gained Football League experience with loan spells at Plymouth, Notts County, Yeovil, Portsmouth and Crawley.