Positive discussions are believed to be ongoing regarding a possible season-long loan agreement for Chelsea forward Moses - who is also of interest to West Bromwich Albion.
The Nigeria international, who moved to Stamford Bridge from Wigan Athletic in August 2012, is yet to figure for Jose Mourinho's Blues so far this season.
Liverpool would welcome the opportunity to add Moses' creativity to their ranks, as Brendan Rodgers looks to build on a productive opening to the season which has brought back-to-back 1-0 successes.
The Reds boss is also working hard to bolster his defensive options before Monday's transfer deadline.
With the vastly-experienced Kolo Toure having picked up a knock during a Capital One Cup clash against Notts County on Tuesday, and with new arrival Aly Cissokho facing up to six weeks on the sidelines, reinforcements have become a top priority.
Highly-rated Sporting Lisbon centre-half Ilori has been heavily linked with a switch to Anfield for some time now, with Sky Sports sources revealing on Friday that a fee had been agreed for his services.
It is understood that the 20-year-old has travelled to England to undergo a medical and finalise a move.
Ilori could soon find himself playing alongside Paris St Germain defender Sakho.
The 23-year-old France international has grown frustrated at a lack of regular first-team football in the French capital and has publicly expressed a desire to move on.
PSG were initially reluctant to discuss the sale of a player who graduated out of their academy system, but Sakho is also believed to be on Merseyside to discuss personal terms and undergo a medical.