The 31-year-old initially joined Leeds United 18 months ago.
The 31-year-old defender had an up-and-down season last term and the arrival of Kyle Bartley on loan has prompted questions regarding his role under new boss Garry Monk.
Bamba, who has spent the past 18 months at Leeds, could still be of use to the Whites but The Sun (reported via The Star) have suggested that Monk might ship him out.
The report goes on to claim that Leeds would accept somewhere in the region of £500,000 for the Ivory Coast international, whose wages may prove a problem in securing a new club.
United's first Championship game of the season comes on August 7 with a visit to Queens Park Rangers, and Bartley might well line up alongside Liam Cooper in central defence regardless of whether the former Paris Saint-Germain man remains at the club or not.
Leeds have had a very decent summer, signing six players between loan and permanent deals thus far, while the departures of influential players has been minimal.
They lost Lewis Cook to Premier League side Bournemouth already, while Mirco Antenucci was released, but the current squad is looking a lot stronger compared to the one Monk inherited from Steve Evans - who did not have a summer transfer window as Leeds boss - and keeping an experienced head like Bamba may be wise.