The two Premier League sides will go head to head at Anfield, starting at 7:55pm and screened by BBC One.
United, however, will miss out on live coverage of an FA Cup tie for the first time since January 2005, when Sir Alex Ferguson’s side drew 0-0 at home to Exeter City in the third round.
Derby are the visitors to Old Trafford for the 2018 third round tie, which will be played at 3pm on Saturday January 6.
Saturday’s action will see Leicester face a potential banana skin away to either Fleetwood Town or Hereford, kicking off at 12:45pm and again broadcast live on BBC One.
Premier League champions Chelsea head to Norwich later in the afternoon, with the 5:30pm kick-off shown by BT Sport 1, which will also screen FA Cup holders Arsenal’s trip to Nottingham Forest at 4pm on Sunday January 7.
Brighton’s home tie against Crystal Palace has been selected for the Monday evening slot, which will see video assistant referees trialled for the first time in competitive action. The recent Premier League fixture between the two rivals was, though, marred by crowd trouble.
Other live third round ties are West Ham’s trip to Shrewsbury at 2pm on January 7, screened on BBC One, while Newport’s home game against Leeds, kick-off at 12pm, will be broadcast on BBC Wales.
Clubs selected for the televised ties on either BBC One or BT Sport will receive £144,000 from the FA’s broadcast fund.