Liverpool followed their title challenge of 2013/14 with a frustrating season last time out, finishing sixth in the Premier League while exiting both domestic cups at the semi-final stage.
Henderson, who is training with England ahead of a friendly with Ireland and European Qualifier against Slovenia, says Rodgers has been instrumental in his development as a footballer after initially struggling following his £20m move to Anfield from Sunderland.
And he insists Rodgers, who this week lost backroom staff Colin Pascoe and Mike Marsh in the wake of Liverpool’s indifferent season, is the right man to revive the club’s fortunes next term.
“Of course I want him to stay” said the midielder. “I have spoke highly of Brendan ever since he came to the club. He has been fantastic for me and for Liverpool.”
“This (coming) season is a big season for everyone involved. We all know that. We want to be finishing high as possible in the league and winning trophies.
“We have a great group of lads with great potential but I think it’s time now we started showing that potential in the Premier League and also in cups.
“Getting to semi-finals is great but we need to be getting to finals and winning trophies. That is what we will be looking to do next season.”