Bamba played 19 times for the Whites last season and became an instant fans favourite.
United had offered a deal to Bamba last month, however this initial move was rejected.
But the club are keen to tie up a deal soon to fight off any interest from Championship rivals Middlesbrough.
The 30-year old made 55 appearances, netting four times for the Foxes between 2010 and 2012 before moving to Turkey to sign for Trabzonspor.
Few Foxes fans will have forgotten Bamba’s debut, where he scored with his first touch for the club in the 2-2 FA Cup draw with Manchester City.
Middlesbrough are reportedly monitoring the situation.