Downing said: "I was disappointed by what was said but if that's the way the manager sees it, I have to take it. That's fine. I'll fight, I'll fight every day.
"I haven't even considered the idea of leaving. I've got three years left on my contract and I intend to see that through. In fact, I want to stay even longer than that.
"I love playing for Liverpool and it's a great club with great fans. I don't want to play for anyone else."
Downing has only started one Premier League game for Liverpool this season.