The USA international forward has been the subject of interest from Anfield for much of the summer, particularly since Brendan Rodgers was appointed manager.
Despite Rodgers making that interest public at a press conference in July, no formal bid has yet been made for the 29-year-old.
That led the west London club to lodge an official complaint with the league last month, which has been discussed among the board but no action has yet been taken.
Fulham left him out of their squad for their opening game of the season, the 5-0 win over Norwich City last Saturday, and he has again been excluded from the group which will travel to Old Trafford to face Manchester United this weekend.
The Premier League stated: "The Premier League has received a complaint from Fulham FC regarding certain comments made by Liverpool FC officials and is currently looking into the matter."
Dempsey had his best ever season during his five-year spell at Fulham last term, scoring 17 league goals to help the Whites finish ninth in the table in Martin Jol's first season in charge.
Jol is frustrated by Liverpool's conduct and feels a distracted Dempsey is unfit to play once more.
"It's the same situation. There has been no formal bid on the table and nothing has changed," Jol said.
On July 18, the same day as an erroneous report claiming Dempsey had signed for Liverpool was broadcast on an American sports news network which is owned by Liverpool's proprietors but unconnected with the club, Rodgers revealed the club's interest in Dempsey.
He said: “Clint is a player we've inquired about, it is as simple as that.
“Ian Ayre, our managing director, has spoken with the club to see what the position is. That is where we're at. He's a very talented player but we don't like to talk about other clubs' players.”