The Northern Irishman met with the Reds’ American owners prior to the 2-2 draw with Aston Villa, with discussions regarding transfer business believed to have been a priority.
Salah has been the Merseysiders’ top target for some time, but they have been unable to tie up a deal as rumours of his valuation fluctuate from day to day.
Rodgers has been keen to press ahead with a deal for a while, and has now been given permission to launch a concrete £8m offer.
Despite speculation of a £16m valuation from the Swiss club, Liverpool are hopeful that their offer will be successful, with the player himself said to have set his heart on a switch to Anfield.
Salah is seen as the ideal man to keep the club’s top four push on track by Rodgers, who is desperate to give his side more options in the final third.
The man dubbed ‘the Egyptian Lionel Messi’ has been in excellent form this season, netting two key goals in the Champions League against Chelsea.