The Parkhead side are scouting potential replacements for Moussa Dembele should the French striker move on during the January transfer window.
Argentine striker Di Santo is said to be high on the club’s list of targets. The 28-year-old has made 19 appearances in the Bundesliga this season.
He spent five years in English football earlier in his career. Signing initially for Chelsea, he then spent time on loan at Blackburn Rovers before his most productive spell in the English Premier League, a three-year stint with Wigan Athletic.
He was an unused substitute as the Latics shocked Manchester City to win the FA Cup, though left in the summer to join Werder Bremen after Wigan’s relegation from the top flight.