The Bhoys defender could be at the centre of a tug of war for his services this summer, with Premier League clubs not helping the situation.
Celtic's Efe Ambrose in action with Heart of Midlothian's Alim Ozturk
Celtic's hopes of keeping defender Efe Ambrose in Glasgow during the early part of the season may rely on whether Premier League stars John Obi Mikel and Odion Ighalo will be released for the Olympics, according to a report in the Herald Scotland.
Apparently, it isn't clear whether Chelsea midfielder Mikel will be free for the tournament, even though he is lined up to captain the side, while Olympics coach Samson Siasia has said Watford are not willing to release Hornets star striker Ighalo.
Odion Ighalo celebrates after scoring for Watford
However, the Bhoys would have their own reluctance at releasing powerful centre back Ambrose for the Rio games, even though he is perhaps not as integral to Celtic as Chelsea or Watford's Nigerian internationals are to them.
With the Scottish champions set to feature in Champions League qualifiers while the Olympics are underway, it could be that Rodgers will see his back line even more depleted than it already is.
A separate Mail report indicates that Siasia was eager for Ambrose to travel to the US training camp as part of a preliminary squad, but that the former Liverpool boss was reluctant to sign off the defender's departure, with fellow defenders Jozo Simunovic and Dedryck Boyata struggling with injuries.
Celtic's Dedryck Boyata (2nd L) celebrates scoring their second with Jozo Simunovic (L), Efe Ambrose (2R) and Scott Brown (R)
Clubs are not obligated to release players for the 2016 Olympics, but Celtic will be eager to remain in the good books with football federations, especially those with international schedules that are often at odds with Scottish fixtures, such as Nigeria. Equally, if players themselves are withheld from playing in international tournaments against their will, it could cause problems with the club.
Ambrose featured 31 times for Celtic last season, failing to start any of the Champions League qualifying matches last summer, but he did feature from the bench on three occasions.
Such are the defensive issues for Rodgers, it is very likely that Ambrose will be called upon in the upcoming qualification rounds, if he remains in Scotland.
Celtic's Efe Ambrose in action with Aberdeen's Shay Logan