Henderson injured lateral collateral knee ligaments during the quarter-final first leg draw with Borussia Dortmund on April 7 and was ruled out for up to eight weeks.
That put his availability for Euro 2016 in serious doubt, but Klopp insists Henderson will be ready in time for the tournament in France.
“I don’t know exactly but he was really celebrating yesterday after the game,” said Klopp, the day after Liverpool beat Villarreal in their European semi-final.
“I saw in his eyes he thinks he has a chance (of being fit for the final), so that’s the first and most important step in the right direction.
“To play in the final on the Wednesday after the season, I think the latest moment - after a long break - when you should be available is the Sunday before.
“But Hendo is in a really good way so it’s good for England. There’s no doubt about being fit for the European Championship.
“The same with Divock Origi but we will see. I have no idea, to be honest.”
Hodgson should also be able to select a fit and in-form Daniel Sturridge after the striker scored his fifth goal in his last seven matches.
The 26-year-old is likely to be rested for tomorrow’s visit of Watford but Klopp is delighted with the progress Sturridge has made since returning to fitness after a hip operation last May.
“It’s not about being careful,” added Klopp.
“All together, with Daniel involved, we have done everything we could to make him as fit as possible and now he is at the highest level.
“That’s really perfect news I think for England and the European Championship.
“We have tried to do our best with and around him.”
For his part, Watford manager Quique Sanchez Flores remains relaxed about his position but will hold further talks with the club in the next few weeks.
Since his appointment last summer, Spaniard Flores has led the Hornets to mid-table security in the Barclays Premier League and also to the semi-finals of the FA Cup at Wembley, where they were beaten narrowly by Crystal Palace.