Downing has fallen out of favour at Liverpool under Brendan Rodgers, who publicly questioned the midfielder's desire to "fight" last week.
The England international hasn't started a league match since the opening day defeat at the hands of West Brom and has failed to make the bench in recent weeks.
Rodgers has overseen a number of departures since taking charge of Liverpool, with Charlie Adam securing a move to Stoke and record buy Andy Carroll now on-loan at West Ham.
There has been speculation Downing could be set for a January exit but the former Middlesbrough and Aston Villa wide man is eager to battle for a place in the Liverpool side and is keen to prove his worth to Rodgers.
"I've got three years left on my contract and I'm going nowhere," said Downing. "I will fight and I am here to see my contract out and I'd love to stay longer. I've worked hard to get here, so I don't want to leave in a rush."