The Reds face Newcastle United away on Monday 27 December, after our previous two Premier League matches against Brentford and Brighton were postponed due to a rise in COVID-19 cases.
Carrington was closed for a number of days as a result, although the players have made a staggered return to training this week.
Rangnick revealed that, after having only 11 players available seven days ago, he now has virtually a full complement to choose from.
Paul Pogba, who is still recovering from an injury picked up while on international duty with France in November, is the only Red still absent, according to the German.