The Merseyside outfit have activated the €22 million release clause of Shakhtar Donetsk midfielder Henrikh Mkhitaryan, but face strong competition from Borussia Dortmund for the Armenia international's signature.
Rodgers, who guided Liverpool to a seventh-placed finish last season, has revealed that he is also targeting a new defensive signing.
|16/1||Liverpool are 16/1 with Coral to win the title next season
"Certainly another attacking player will really benefit us, and probably another defender. We'll see how it develops over the course of the next few months."
Liverpool have already completed moves for Kolo Toure, Luis Alberto, Iago Aspas and Simon Mignolet and Rodgers believes his side's fast start to the transfer window should make the initial stages of next season easier.
"It's great - it's a big thing to the club because we looked at last summer and there were lots of things that were difficult for us," said Rodgers.
"That meant that the opening period of the season was difficult.
"From that we've got all our people involved, our recruitment team in - and they got to work as soon as they came in.
"We brought great signings in in January and that's really helped us. Obviously the plan was to get our signings in as soon as we possibly could - and we still hope to make a few more.
"I'm very happy with the four players I've brought in, and they'll add to the group."