Huddersfield Town could face a repeat of the Shankly Trophy match played three weeks ago in the next round of the EFL Cup, should the Terriers overcome Shrewsbury on Tuesday.
Liverpool will play their EFL Cup second-round match away from home, regardless of the draw due to expansions to Anfield and Town could face the Reds for the second time in a month.
The previous clash between the sides drew a capacity crowd of 21,266 to the John Smith's Stadium, with Liverpool emerging 2-0 victors.
The Reds are expanding the Main Stand at Anfield and do not play a home game in the Premier League until the visit of Leicester on September 10.
They have two away games - at Arsenal and Tottenham - and have reversed their home fixture with Burnley before they face the champions
An EFL spokesman said: "The board has considered a request from the club and felt that that due to the unique circumstances they face at this particular time, it was appropriate to agree to the reversal.
"Compensation will be paid by Liverpool to the opposing club should they be drawn at home, to be determined by the EFL board."
The draw for the second round will take place after Aston Villa's match against Luton Town, which is due to finish at around 10pm on Wednesday, with Premier League clubs joining the lower league hopefuls in the pot.
Before then, Huddersfield Town must navigate a tricky fixture against Shrewsbury - a lower league side with a strong record in cup competitions.