The Liverpool captain, 25, suffered knee ligament damage against Borussia Dortmund on 7 April, and was expected to be sidelined for up to eight weeks.
However, Klopp says Henderson may feature in the Reds' Europa League final against Sevilla on 18 May.
"Hendo is in a really good way so it's good for England," Klopp said.
"There's no doubt about him being fit for the European Championships."
Read: Oxlade-Chamberlain ruled out of Euro 2016
Klopp says Henderson must play in Liverpool's final Premier League match of the season against West Brom at The Hawthorns on 15 May to be considered for the final against Sevilla in Basel three days later.
"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," the German said.
England manager Roy Hodgson, who names his 23-man squad for Euro 2016 in France on 12 May, has already said he is reluctant to include players who are not match fit.
"I wouldn't be happy to really take players with us in the hope they will become fit during the tournament," he said in November 2015.
England begin their Euro 2016 campaign against Russia in Marseille on 11 June, then meet Wales in Lens on 16 June and Slovakia in St Etienne on 20 June.
England midfielder Jordan Henderson will be fit for this summer's European Championship finals, according to Liverpool manager Jurgen Klopp.