The French defender is expected to agree a deal until 2020.
The Frenchman made his first appearance of the season for the club in Thursday's 1-1 draw with Bordeaux in the Europa League, where after the game he described himself as a 'Liverpool soldier', which could have been read as him reaffirming his commitment to the club's cause.
There had been talk that Sakho would stall on any such discussions, according to one article in the Daily Mail, until he received assurances over his playing time after he was omitted from the most recent France international squad. The player is obviously keen to be part of the side's Euro 2016 campaign, with France hosting the tournament next summer.
In the opening five games of the season he has found himself behind Martin Skrtel and Dejan Lovren in the pecking order and one would think that he would not be committing to a new deal if he had not been given the assurances that he would be getting a decent run of games in the side, especially in the wake of recent defensive displays against West Ham and Manchester United.
The Liverpool Echo report says the new deal commits him to Anfield until 2020, and manager Brendan Rodgers has said he is contention for Sunday's Premier League clash against Norwich City following his display in France, and prior to the game said he was part of his plans for the future.
What will be interesting now is to see who, if anyone, is dropped to allow Sakho to come back into the side and whether that will be part of a back four or a back three - which the Reds deployed in the Europa League.
One would also wonder about the impact giving him the captain's armband for the game against Bordeaux had on the player, in terms of highly thought of he is at Anfield. There is now a general feeling among supporters that he is the best central defender at the club and should be given an extended run in the side at the expense of either Skrtel or Lovren.