The Reds faithful had to witness one of their beloved former managers join a rival club in the summer when Benitez succeeded Carlo Ancelotti at Everton, which left a bad taste in the mouths of some on the red side of Merseyside.
Liverpool fans could see another of their former bosses join another rival before the end of the season with Rodgers claimed to be favourite to replace an under pressure Ole Gunnar Solskjaer at Manchester United.
However, Reds legend Thompson has dismissed notions that Rodgers taking over at Old Trafford will have same effect on fans as Benitez joining Everton as he feels the 48-year-old was never fully committed at Anfield.
But Thompson lauded the Leicester City boss as a fantastic manager and feels he would do a great job at Manchester United if they hire him.
Asked whether he thinks Rodgers joining Manchester United would leave a bad taste in Liverpool fans’ mouths, Thompson told Off The Ball: “Well I do not think he was ever committed, was he?
“I mean as a Liverpool fan he did fantastic for Liverpool, absolutely brilliant.
“I do not think it would be that same thing as Rafa Benitez going to Everton after what Rafa Benitez did.
“But Brendan Rodgers, I wish him the best of luck.
“I think he is a fantastic coach; he is a really good guy and I think he would really do well for Manchester United.”
Rodgers has insisted he is fully committed to the Foxes at the moment but many believe he will take the Old Trafford hot-seat if Manchester United part ways Solskjaer and approach him with an offer.