Klopp has vowed both he and his senior players will not be in attendance for the Anfield clash with Shrewsbury Town, provisionally scheduled for next midweek during their winter break.
An FA statement read: "The FA went to great lengths to create an annual mid-season player break, working closely with the Premier League and its clubs.
"It is a new and significant addition to the English football calendar and is designed to benefit clubs and their players.
"This allowed the Premier League room in its calendar to have a split round of fixtures over two weekends.
"Prior to start of the 2019/20 season, all clubs accepted that Emirates FA Cup fourth round replays, where required, would have to take place during the first week of the mid-season player break.
"This will only affect a small number of clubs due to the split of Premier League fixtures in the mid-season player break."