The former Wigan Athletic, Blackburn Rovers and Chelsea player struggled in the English game, but Bhoys’ boss Brendan Rodgers believes he could be successful in the Scottish Premiership.
Di Santo is being lined-up as insurance if a late bid arrives for Moussa Dembele, according to reports in Germany.
The 28-year-old has lacked an end product for most of his career, averaging just one goal every six games.
He failed to score in 16 games for Chelsea, and one goal in 24 appearances during a loan spell with Blackburn highlighted his wastefulness in front of goal.