The Scottish champions have previously rejected bids for Ambrose.
Picture Supplied by Action Images - Cetic's Efe Ambrose
The defender has failed to impress at the club since arriving from FC Ashdod back in 2012.
He has also failed to adequately fill the gap left by Virgil van Dijk, who departed to join Southampton last summer.
Celtic's Efe Ambrose (L) in action with Salzburg's Massimo Bruno
Fans and pundits alike are not convinced he is good enough, and earlier this month saw him heavily criticised when Gibraltarian minnows Lincoln Red Imps beat Celtic in the Champions League.
Indeed, he was axed from the squad that beat the same side 3-0 in the second leg this week, likely because of his error in the first leg.
Celtic's Efe Ambrose in action with Heart of Midlothian's Alim Ozturk
The club had previously been determined to keep hold of him though as they rejected bids from Olympiacos and Maccabi Tel Aviv.
However, they have now changed that stance according to the Daily Mail, and are willing to sell him should the right offer be made.
Their change of heart suggests that adding a new centre back may be among Brendan Rodgers chief concerns this summer.
Celtic's Efe Ambrose looks dejected at the end of the match