The Cottagers approached the
However, Rodgers insisted the club had made its response privately to the Premier League and would not be commenting any further.
"For me there is nothing to say on it," said the Northern Irishman.
"This was something I was aware of a number of weeks ago. That has been dealt with in-house."
Liverpool has distanced itself from suggestions it wanted to sign Dempsey but one player set to arrive at Anfield - on loan - is Real Madrid midfielder
"I believe, from the club, everything has been organised and sorted in terms of paperwork so we're hoping in the next 24 hours that can be done," added Rodgers.
"He is a great technician. He was player of the season in
"He got a move to Real Madrid and obviously through injury it has not quite worked out for him.
"But he is a wonderful player technically and tactically who understands the game and we hope his extra quality coming in will help the group."
Liverpool manager Brendan Rodgers fully expects star striker Luis Suarez to be at the club next season.