Reds boss Brendan Rodgers is desperate to add more firepower to his squad during the January transfer window to help ease the pressure on main goalscoring threat Luis Suarez.
Liverpool are believed to have sent scouts to run the rule over Jeffren in recent weeks and are ready to make a move in January.
The former Barcelona youngster who joined Sporting last year was reportedly a target for Liverpool while former boss Kenny Dalglish was in charge.
Jeffren has fallen out of favour in Lisbon and could complete a loan switch to Anfield when the winter window opens.
Liverpool are certainly short of attacking options following Andy Carroll's departure and Fabio Borini's injury, and while the 24-year-old isn't an out and out striker he would certainly add some creativity to the Reds' attacks from out wide.
According to Record, Liverpool have already made their interest known to Sporting and a deal could be wrapped up by the Merseyside club in the coming days.
According to the paper it is hoped that he and Luis Suarez will strike up a rapport and help fire Liverpool up the Premier League. If completed, the move would likely see Jeffren see out the remainder of the season at Anfield, with an option to make the switch permanent in the summer.