Mensah – still only 29 – was released from his contract at Lyon at the end of last term after failing to make a single top-team appearance last season for the Ligue 1 outfit.
A combination of injury and the lack of trust from Lyon’s contributed to his season in the shadows even though he was key for Ghana at the Africa Cup of Nations.
Now coach Lennon must weigh up Mensah’s abilities, wages, fitness and reliability ahead of taking the deal beyond first base.
Celtic are in desperate need of a dominant centre-half and on the face fit Mensah – dubbed the “Rock of Gibraltar” – fits the bill.
Prior to last season Mensah spent two seasons on loan at Sunderland and made 34 appearances for the Black Cats.
He hoped to secure a permanent switch, but the deal could not be completed and he then returned to France and endured a miserable season.
Now as a free agent he’s able to negotiate with any club and Celtic have been made aware of his salary level and willingness to play.
The big question mark surrounds his ability to last a season because of injuries – it was an issue during his days at Sunderland and then affected his chances in France last term.
Turkish outfit Tranzonspor and French side Bordeaux have also been linked with the defender who started his senior career in Italy with Chievo before working his way to Rennes and then Lyon in France.
Celtic’s defence was ripped to shreds by Ajax on Saturday in Amsterdam and Lennon is keen to add players before next week’s Champions League qualifying tie with HJK Helsinki.