Rodgers' side will face Queens Park Rangers in west London and England manager Hodgson intends to attend the game.
As such, the Three Lions coach will seek the Northern Irishman out to discuss the now infamous Raheem Sterling situation.
The 19-year-old Liverpool and England winger apparently complained to Hodgson that he was tired and didn't want to start for the national team against Estonia.
Meanwhile, striker Daniel Sturridge, who could feature at QPR after returning from a spell on the sidelines with a thigh injury, will also be discussed by the two coaches.
Sturridge picked up his injury while training with the England squad and Rodgers had implied that the national setup could have handled the 25-year-old's fitness better.