Henderson has missed the last four league games for the club after picking up a hamstring injury in Liverpool's 3-3 draw with Arsenal last month.
"Virgil trained well," Klopp told a news conference on Friday. "Hendo had a clearing session today and should be fine from tomorrow."
Klopp is also monitoring the fitness of defender Ragnar Klavan and forward Mohamed Salah but said the duo should be available for the trip to the Liberty Stadium.
Liverpool beat Swansea 5-0 when the two sides met at Anfield on Boxing Day but Klopp believes his team face a big challenge in the return fixture after manager Carlos Carvalhal took charge of the Welsh side.
Swansea, who are bottom of the table with 17 points from 23 games, beat Watford 2-1 in Carvalhal's first league game before suffering a 2-0 home defeat to Tottenham Hotspur and then held Newcastle United to a 1-1 draw last weekend.
"We played against (the team at) the top of the table and it was a fantastic game. We played Swansea a few weeks ago and the game was much more difficult than the result could let you think," Klopp said.
"We know about the specific challenge in this game because they are now bottom of the table but they are in a good way... It will be different."
Liverpool are third in the league, level with fourth-placed Chelsea on 47 points and are unbeaten in 14 games.
(Reporting by Shrivathsa Sridhar in Bengaluru)
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