The Liverpool owner has said they are "focused on winning the Premier League next season" after Jurgen Klopp's side clinched their sixth European title earlier this month.
John Henry's company Fenway Sports Group bought the club from Tom Hicks and George Gillett in 2010. They were narrowly pipped to the English title last season by Manchester City - falling short by just one point.
They were still in the title race on the final day and gave themselves the best chance of winning the Premier League with a 2-0 win at home against Wolves, however, it was not enough to stop Pep Guardiola's men who sealed their second title in a row with a 4-1 victory away to Brighton.
The Merseysiders took home the Champions League title with a 2-0 win against Tottenham Hotspur at the Wanda Metropolitano in Madrid. Egyptian international Mo Salah and Divock Origi getting the all-important goals.
Henry has said, "to me winning in Europe is bigger than winning in England but I think it's true the fans want it. I know we're going to be focused on winning the Premier League next year."
"Our guys gave it their all from the first day of the season to the last. It's a long season, they played up to their capabilities and just gave so much effort.
"It didn't matter who the opponent was, they out-ran every opponent and I felt they deserved to walk away with a trophy. We walked away with the biggest one so I'm very happy."
The 69-year-old Liverpool owner also spoke about the speculation surrounding the future of Origi, who scored two goals against Barcelona in the semi-finals and in the 87th minute of the final of the Champions League.
The Belgian international's contract runs up next year and had been a doubt to stay with the English club before what some describe as a resurgence of his career in the latter end of last season.
Henry has backed the 24-year-old striker to keep improving his form and play more in the red of Liverpool, saying "it's not up to me but I would guess we will see more of Divock next year."