Rodgers has built up a rapport with the Blues after managing youth and reserve teams at the club in the past, and has stated that he is eager to get the midfielder on board.
"We have an agreement with Chelsea, but they have one or two injuries so we are just waiting to hear when he will be allowed to come. The important thing is we have found an agreement, which is fantastic," Rodgers told Sky Sports News.
"It's been a process and we have to respect he is a Chelsea player and as much as we would like to have him here, there is more to it than that. He is obviously a talent and they want to be sure that they let him out at the right time."
McEachran has made 22 appearances for Chelsea since breaking into the first team in 2010.