The German defender has played just once for the Hoops, in a Scottish Cup match against Morton in March 2018.
But the former RB Leipzig defender, who was summarising for a TV station in his homeland when the Bundesliga side came to Celtic Park on Europa League duty, is yet to make a league appearance for the Hoops - and likely never will.
The acquisition of Compper, who reportedly cost the club £1 million nearly 12 months ago, came up as a topic at Celtic’s AGM this week.
The 33-year-old has struggled with injury, but has also found it hard to regain full fitness, according to Rodgers.
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The Northern Irishman continued: “Marvin was brought in to provide experience but he has struggled for fitness and the unpredictability of his fitness has played a part.
“If anyone is to blame then blame me.
“Marvin is an extremely professional player and it’s an emotional time towards the end of your career. He has been a great help to the younger players.”
Compper’s contract with Celtic runs until 2020, but it remains to be seen if the one-time Germany international is kept on.