Downing dismissed claims that the ongoing speculation over Suarez's future is having a detrimental impact on Liverpool's pre-season.
He said: "What's going on with Luis isn't a distraction. Pre-season has gone really well and we've got some good results. Now we want to really push on.
"Since he came back Luis has been training really well and I think whatever happens with his Liverpool future will be sorted out in the next week or two.
"We want to keep our best players to help us get into the Champions League. That has to be our aim. We've strengthened the squad with new signings and I'm sure there will be a few more to come.
"If we can reproduce the form we showed in the second half of last season, we'll have a good chance of breaking into that top four.
"We want Luis to be part of that. He's a top player, one of the best in the world - we saw that with the goals he scored last season."