Midfielder Henderson has been sidelined for two weeks with a foot injury, while Cameroon defender Matip has been out of action for a month with an ankle problem.
The Liverpool Echo says both players will return to full training at Melwood on 12 January and – barring any unexpected setbacks – both should be available for selection at Old Trafford on 15 January.
The news is a major boost for Liverpool manager Jurgen Klopp, whose team are yet to win a game in the 2017 calendar year.
The Reds were held to a 2-2 draw by Sunderland in their last league outing and followed that up with a goalless draw with Plymouth Argyle in the FA Cup third round.
Neither Henderson nor Matip travelled with the Liverpool squad for the EFL Cup semi-final first-leg defeat against Southampton at St Mary's on 11 January.
Nathan Redmond's first-half goal gave the Saints control of the tie going into the second leg on 25 January.
The visitors were dominated for much of the match, and Klopp admitted that the margin of defeat could have been greater.
"It could and should have been 2-0, 3-0. The best thing for us is the result. We know that we can play better at Anfield, nothing is decided," the German coach told the BBC.
"We cannot be happy with the performance, Southampton cannot be happy with the result. I can't remember a clear chance for us.
"We gave the ball away so easily and we needed Loris Karius to save our lives two or three times.
"We have to show a reaction – but it would be cool if we could already show a reaction at the weekend, because we probably need a better performance to get something at Old Trafford."
Liverpool are second on the Premier League table, five points above sixth-placed United.