Having taken over from Kenny Dalglish a few weeks ago, the Northern Irishman wants to put his stamp on the squad and players such as Joe Allen and Clint Dempsey have been reported as targets.
Fulham's US midfielder is trying to push through a move to Anfield and decided not to travel with his club to their pre-season camp in Switzerland as exclusively revealed by Goal.com earlier this week.
Despite this development, Rodgers has opted not to reveal the names of any of his potential signings for fear of being out-priced in the market.
Rodgers told the club's official website: "There's a lot of great work going on, obviously with the board and Ian Ayre in particular doing a lot of work behind the scenes.
"I've got regular contact going with our American owners and, in particular, Mike Gordon from Fenway Sports Group.
"Obviously when it's a club like Liverpool prices are always increased and so on, but I always felt it was important by the beginning of the season we could have the squad we want - and certainly by the end of the transfer window I would hope that will be the case.
"There is lots of speculation. I've seen hundreds of names linked with Liverpool and there's very few of them that were even close to coming here or we have even looked at.
"Unfortunately for the supporters they've got to read it and put up with it. But the message is there is a lot of work going on, on a number of deals and hopefully we can get those completed by the end of August."