Cheika, 56, was in charge of Australia's men's rugby union team for five years, and is currently coaching Argentina at the Rugby World Cup in France.
But his contract with Argentina ends after this tournament, leaving him a free agent.
The Herald says the Tigers have "reached out" to Cheika to gauge his interest in potentially joining the embattled NRL club in an official capacity.
Tim Sheens was general manager of football before taking on the head coach role at Concord this year, but that ended miserably with a last-place finish and Sheens leaving the club before the season had finished.
The Tigers are desperate to turn their on-field fortunes around, having not played finals in 12 years in cycled through head coaches at an alarming rate in that time.
Benji Marshall has taken the coaching reins but the club remains without an experienced football person above him, and Cheika has plenty of experience in multiple codes, having also worked with Roosters coach Trent Robinson previously.
The Herald says former player Mark O'Neill was on Monday recommended to the Tigers board for the football manager position, but he would need to be lured away from his role at Parramatta.
Stream the NRL premiership 2023 live and free on 9Now
If the O'Neill approach falls through, Cheika is being sounded out for a job at the NRL club.
O'Neill played for the Tigers alongside Marshall when they won the 2005 premiership, with Sheens as coach.
The Herald reports the Tigers also approached Knights football manager Peter Parr, who declined to jupm ship.