The Cottagers approached the Premier League to express their unhappiness with what they felt was their public pursuit of the United States international.
Fulham manager Martin Jol feels Dempsey has been distracted by the speculation and having left him out of the squad for last weekend's opening fixture he will do the same again tomorrow [Saturday].
However, Rodgers insisted the club had made their 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 have distanced themselves from suggestions they wanted to sign Dempsey but one player set to arrive at Anfield - on loan - is Real Madrid midfielder Nuri Sahin.
"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 Germany, captain of Dortmund and fantastic at a very young age.
"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."
With Andy Carroll relegated to the bench - at best - in Rodgers' new system, his two main attacking options up front are Luis Suarez and Fabio Borini, neither of whom are considered to be purely goalscorers.
Champions Manchester City, the visitors to Anfield on Sunday, have an embarrassment of riches on the forward line with the likes of Carlos Tevez, Sergio Aguero and Edin Dzeko.
Manchester United have new £24m signing Robin van Persie and Wayne Rooney, Arsenal have Olivier Giroud - France's leading goalscorer last season - while Chelsea have Torres.
"It is no good having a goalscorer scoring 30 goals and no-one else scores - I've always been against that theory," said the Reds boss.
"You are going to need upwards of 70-odd goals to be up around the Champions League [places].
"For me it is a team ethic. Luis Suarez will score goals, Steven Gerrard can score goals, young Fabio Borini will score goals - but we also need goals from our centre-halves.
"If you can get your centre-halves scoring five goals that will always add and then you are looking at your full-backs doing a bit more.
"It is a team responsibility, not just one player. You bring in one striker who can score you goals, which is great, but it's not good for the team if the rest don't score.
"For us it is trying to have players in different areas of the field who can cause a problem.
"But equally important is that at the other end you are not conceding goals.
"I think we have shown, apart from last week (in the 3-0 defeat at West Brom) when the game was broken when we went down to 10 men, that we have a good mindset and been strong this year."
Last season Liverpool hit the post or crossbar more than 30 times and missed seven of 11 penalties.
Rodgers said that could not be allowed to happen again and he had drummed into his squad they had to be sharper in front of goal - although Borini looks like he still has some work to do after firing against a post with only the goalkeeper to beat in last night's [Thursday] 1-0 Europa League play-off win at Hearts.
"I told the players this year you can't blame referees and crossbars, you have to be clinical, you have to be ruthless," added the Northern Irishman.
"We will always create enough chances but even if we don't, if there are only one or two chances as in big games it is tight as defences are harder to break down, when you do get those chances you have to put them away.
"It is something I have reinforced since I came in here: it really is about ruthless simplicity.
"When you get chances you have to take them but I believe I have a number of players who can score goals.
"We just have to make sure we keep arriving in the areas and not get disappointed.
"It might be goalless for 90 minutes and come in the last minute but you have to keep going and keep pushing and wait for that moment to come and when it comes you have to exploit it."