The former Bolton Wanderers defender - out-of-favour at Anfield and widely tipped to leave Merseyside this summer - won two caps under now-Foxes boss Sven Goran Eriksson during his reign as England coach. Konchesky has not appeared for the Reds under Kenny Dalglish and was loaned to Nottingham Forest - also tipped to be interested in securing his signature - for three months last term.
Meanwhile, Newcastle winger Wayne Routledge is also on Eriksson's radar, the Leicester Mercury reporting that he is close to agreeing a deal that could see him arrive at the King Power Stadium within 48 hours. Like Konchesky, Routledge is believed to have been subject to a £1.5 million bid from Leicester City's Thai owners and the 26-year-old former England starlet is rumoured to have accepted terms with the Foxes ahead of Forest, Queen's Park Rangers, Cardiff City and Swansea City after being impressed by Eriksson's renaissance in the East Midlands.
Talk on signings will have to wait for the Swede, however, as he looks forward to his side's first pre-season friendly in his native country this evening. A Leicester City XI - likely to feature two full sides over 90 minutes - will take on Swedish third-tier outfit IK Sirius at their Student Arena at 6pm BST.