Thompson, who played almost 500 games for Liverpool as a centre back in the 70's and 80's, was also assistant manager to Gerard Houllier at Anfield.
Now a Sky Sports pundit, Thompson believes that current Reds boss Rodgers needs to make a tactical change in order to get the best out of one of his summer signings.
Rodgers snapped up left back Alberto Moreno from Sevilla after the 22-year-old emerged through the ranks with the Spanish club and became a first-team regular.
Tipped as a star of the future at left back, Moreno has had a tough first season in English football, particularly struggling against Arsenal on Saturday.
Moreno was at fault for the opening goal, allowing Hector Bellerin to cut inside and curl the ball beyond Simon Mignolet as Arsenal romped to a 4-1 win.
In Rodgers' 3-4-3 system, Moreno plays as a left wing back - but Thompson told Sky Sports that Moreno should be used as a left back in a back four in order to get the best out of him.
"I think he’ll go with the same system against Blackburn and try to get it working again, but switching to a back four would allow someone like Moreno to take up his natural position," said Thompson.
"In the current formation, he’s always looking over his shoulder and back towards his own goal. He’s much more comfortable when he’s further back, closer to his goal and facing that huge space in front of him to run at," he added.