Johnson has found a new lease of life under Sunderland boss Gus Poyet and is in the middle of a hot scoring streak which has led to calls for him to be called back into England manager Roy Hodgson's squad.
His form has not gone unnoticed at Anfield apparently with Rodgers ready to offer striker Fabio Borini, currently on a season-long loan at Sunderland, as part of a possible swap deal.
Rodgers missed out on Dnipro winger Yevhen Konoplyanka last month and may now turn his attentions to Johnson.