According to Sky sources, positive discussions are ongoing regarding a possible season-long loan agreement for Moses, who is also of interest to West Brom.
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 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, and 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 Saint-Germain's 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.
PSG manager Laurent Blanc revealed that Sakho will leave Ligue 1 with his blessing.
He said: "Sakho is not just anybody at PSG. He has been here, he has lived everything here, he was the symbol of the club.
"I would really have liked to continue working with him but he's signalled his desire to leave the club. The board and himself have found a solution. I wish him good luck."
The France international is yet to play for the club this season with Thiago Silva, Alex and new signing Marquinhos all preferred.