The deal to bring Jaroslaw Fojut from Poland on a Bosman has been pulled after he suffered knee-ligament damage playing for Slask Wroclaw.
With Glenn Loovens saying his farewells to team-mates after his contract ran out, and Daniel Majstorovic not receiving the offer of a new deal either, the need for another strong centre-back is acute. Cha Du-ri is also leaving, along with Mark Wilson, after their contracts came to an end and the club decided not to activate the year option they held on both.
Back-up keeper Dominic Cervi is being allowed to go, while Darren O'Dea and Niall McGinn, too, come to the end of their time at Parkhead.
Lennon will attempt to move around half a dozen others out of the club to make way for new faces, and has just missed out on signing Latvian striker, Artjoms Rudnevs, who opted to move to Hamburg from Lech Poznan in a deal worth £3.5million.
Rosenborg's teenage midfielder Markus Henriksen remains a player of interest. But with several clubs from Germany, France, Holland and France also in the hunt, he could be priced out of Celtic's reach.
Lennon's priority remains to bring in a powerful central defender and a striker who can add aerial threat to their attack.
Mills, captain of Leicester until he had a fall-out with new boss Nigel Pearson in February, could be the man to add strength at the back.
Reports in England claim Kelvin Wilson could be offered in a loan move.
At 25, one-time Manchester City defender Mills has similar experience to Loovens when he arrived at Celtic in 2008 from Cardiff City.
After collecting a Championship medal, the Dutchman is now looking for another club, and said: "I have been here for four years, and it is the end of my contract."
Mills was signed by Sven-Goran Eriksson from Reading in a deal worth £5m a year ago, and the 6ft 3in defender was considered a key-stone of the Leicester side installed as favourites to win promotion back to the Premiership.
But, his relationship with the man who succeeded Eriksson, Pearson, has become strained and a quick exit from the club is anticipated.