Sky Sports sources understand Liverpool are not expected to make any signings before the transfer window deadline.
Fulham accepted Aston Villa's £7million bid for Clint Dempsey on Friday morning, but the player opted against a move to the West Midlands club in the hope of joining Brendan Rodgers' side.
However, the Cottagers failed to agree terms with the Anfield giants for the American, who has scored 50 goals for Fulham in 184 league appearances.
It is understood England international Jordan Henderson was offered as part of the deal to bring 29-year-old Dempsey to Merseyside, but negotiations broke down.
Rodgers left the club's Melwood training headquarters earlier in the evening, closely followed by managing director Ian Ayre, who had been working diligently behind the scenes trying to get deals done.
Liverpool were also interested in the possibility of signing Chelsea striker Daniel Sturridge, but the youngster was named on the bench in the club's Super Cup match against Atletico Madrid in Monaco.
Rodgers has already added names such as Joe Allen, Fabio Borini and Nuri Sahin to his ranks.
However, the Northern Irishman has also lost Andy Carroll on a season-long loan to West Ham, and Jay Spearing, also on a season-long loan to Bolton Wanderers, while Charlie Adam has joined Stoke City in a £4million deal.