The 28-year-old was told by Brendan Rodgers that he could leave the club at the start of last season but he managed to force his way back into the manager's plans.
"I'm here to stay. I'm enjoying it, especially last season when I got a good run in the team. Hopefully that will continue, and I need to work hard," he told the Liverpool website.
"I want it to continue. It's why I came here, to play in a successful team."
Downing also spoke on his chances of playing in the World Cup next summer in Brazil should England qualify.
The winger has not featured in any of Roy Hodgson's recent teams but he remains hopeful that he can force his way back into the national side.
"It's been difficult as I've not played for England over the last year or so, but I'd love to play at the World Cup," he added.
"It's a year away and I've got a full season to get in the manager's thoughts. I'll just take every game as it comes and see what happens at the end of the year."
Liverpool begin their Premier League campaign at home to Stoke City on August 17.