The Reds are readying themselves for a pre-season tour of North America and hope to have extra bodies on board before they jet off.
Rodgers is confident he will have bolstered his ranks prior to Liverpool's departure, with it possible that two acquisitions could be made.
Asked if he expected to have completed a signing before the Reds head to the States, Rodgers told Sky Sports News HD: "We hope so. There certainly won't be as many as has been labelled out.
"I think the reality is that for players to be associated with Liverpool is great, but the reality is that we have only made three or four enquiries about players.
"Hopefully we can close out one deal this week, maybe two.
"Hopefully we can do one and then look to add to it over the course of pre-season."
Reports have suggested that Esteban Granero is a top target for Rodgers, with one approach for the Real Madrid midfielder having already been knocked back.
The new boss at Anfield is keeping his cards close to his chest, though, and will not be drawn on the finer details of his summer shopping list.
He added: "I will never speak about targets or possible players, it's not something I like to do.
"All I will say is that there has been a whole raft of players linked with coming to Liverpool and there is very few of them that are actual targets for us."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.