Oliver, who had a number of incidents to review at Elland Road on Saturday including a nasty-looking foul by Granit Xhaka on Raphinha that match referee Andre Marriner missed completely, will be assisted by Stuart Burt and Simon Bennett at Anfield.
This season Oliver has taken charge of 20 matches, including Champions League contests, and dished out 66 yellow cards and three reds. He has also awarded five penalties.
He was the man in the middle for Leeds' trip to Burnley, when seven players saw yellow in a feisty affair, and refereed Liverpool's 4-0 win over Arsenal.
Liverpool are the club the 36-year-old has refereed the most, the Reds winning 25 of the 48 games with Oliver in charge. He's sent off one Liverpool player in that time, three of their opponents and awarded 12 spot-kicks for and six against them.
Leeds, meanwhile, have won four of their 12 encounters with Oliver as referee. The Ashington official has awarded four penalties to Leeds and two against them, both at Anfield, while sending off four opposition players and no Whites.
Oliver was in charge for Leeds' last visit to Liverpool, a 4-3 thriller of a defeat in which Jurgen Klopp's men scored twice from the spot. He was also the referee who red carded three MK Dons players in a 4-1 2010 victory for Simon Grayson's Whites.
Robert Jones has been appointed referee for Leeds United's December 28 Elland Road meeting with Aston Villa.
His assistants will be Simon Bennett and Adrian Holmes, with Oliver acting as fourth official, Lee Mason as VAR and Matthew Wilkes as assistant VAR.
In nine matches this season Jones has shown 32 yellow cards, awarded three penalties and is yet to send anyone off. He refereed Leeds' home game against Wolves, awarding a late penalty when Joe Gelhardt went down in the area that allowed Rodrigo to rescue a point for Marcelo Bielsa's side. He also pointed to the spot in last season's 1-0 Elland Road win over Burnley.
Leeds are his most refereed club, the Whites winning half of their 12 games with the Merseyside man in charge. He's yet to award a penalty against Leeds and has produced his red card in just two of their matches, sending off Eunan O'Kane in a 2018 Championship defeat by Ipswich and Ben Pearson in a 2019 win over Preston North End.