Lallana’s six-year stay on Merseyside looks set to come to an end after the conclusion of the 2019/2020 season, when he will become a free agent.
The 32-year-old was signed by Rodgers from Southampton during the Northern Irishman’s time as Liverpool boss in 2014.
Lallana’s Liverpool career has been disrupted by injuries in recent seasons, with most of his 40 top flight appearances over the last three seasons coming as a substitute.
Robinson believes Lallana would flourish under Rodgers again if the pair were to re-unite at the King Power Stadium.
“Lallana and Leicester are the perfect fit. Brendan Rodgers brought him to Liverpool so he is obviously a player that he likes and admires,” Robinson told Football Insider.
“That player-manager relationship is there so if he is to leave Anfield this summer Leicester would seem almost a certain option for him, provided Brendan wants him.
“He is a top player and he has a long-while left. He has had a very good time at Liverpool, but he is now of an age where he will not want to be sitting on the bench.
“It is an age where you want to play football. It could be a harmonious transfer for everybody.”
Lallana has won the UEFA Champions League, UEFA Super Cup and FIFA Club World Cup during his time at Liverpool.
Leicester City look set to secure Champions League football for next season as they sat third before the current campaign was brought to a halt because of the coronavirus pandemic.