The Daily Star says Rodgers hopes to pull off the £7m signing of Callejon from Real Madrid in the next few days.
Callejon, 25, scored 13 goals for Madrid last season despite being used largely as a substitute, and fits the Rodgers mould.
A source close to Callejon said last night: "The chance to play for Liverpool is very attractive for the kid. They have made him an offer.
"But it will be up to Jose Mourinho whether he is allowed to leave or not."