West Ham will take on Liverpool at London Stadium on January 29 with a 7.45pm kick off in east London after the Premier League announced the fixture change.
The original match was due to take place on December 21 but was postponed some time ago thanks to the Reds' involvement in the Club World Cup, meaning the Hammers had a 12 day break in between beating Southampton and Boxing Day's loss at Crystal Palace.
The Premier League leaders will now head to the capital for a midweek fixture on a Wednesday night early next year.
Jurgen Klopp's men were out in Qatar for the Club Wolrd Cup and came back with the winners trophy after beating Monterrey of Mexico in the semi final and then seeing off Flamengo in the final thanks to an extra time goal from Roberto Firmino.
They showed no ill-effects of their long trip either on their return to Premier League action on Boxing Day as they swatted aside second-placed Leicester City 4-0 at the King Power Stadium to extend their lead at the top of the standings to 13 points before reaching the halfway point of the season.
The return fixture for the Hammers and Reds at Anfield has already been re-scheduled and moved to an 8pm, Monday Night Football kick off at 8pm on Merseyside on February 24.
There is no love lost between Pellegrini and Klopp, with a rivalry between the pair dating back to 2013 when Pellegrini's Malaga were knocked out of the Champions League at the quarter final stage to Klopp's Dortmund thanks to two injury-time goals.
Speaking after the Hammers lost 2-1 to Liverpool in Stratford last season thanks to two somewhat dubious goals for the visitors, Pellegrini said: "Klopp is used to winning with offside goals.
"He beat me against Malaga with a goal seven metres offside - so he cannot complain about anything.
"They scored a goal one metre offside. And in the last minute with Origi in front of the linesman, again one metre offside."
Who knows however is Pellegrini will be in charge for the game next year as he has just two games to save his job following a dreadful run of two wins in the last 12 games.
