Downing signed for Liverpool for £20 million this summer.
He said: “I have played a few games with him [Carroll] with England and in pre-season and I know his strengths. If you get the ball in the box, then nine times out of 10 he will get on the end of it. He is a big target.
“I have seen a bit of Suárez in the Copa América [for Uruguay] and he was brilliant. He and Carroll will suit each other and there is Dirk [Kuyt] as well who can play up top. If we work at it, then we can strike up a few good partnerships.”