The 30-year-old rejoined the Hammers on a three-month contract last week after being released by the Premier League outfit in the summer.
"He certainly looked good to me," Sky Sports News quotes Downing as saying after playing alongside the striker in a recent behind-closed-doors practice match.
"I've played with Carlton for years at England, he's a strong boy. He certainly looked like he has been working hard, and I've seen that at the training ground. I think he just needs games, games like that to get him fit.
"I think we needed another option. Carlton can bring that. He can also play on the floor, as well as being good in the air, so it's a different option for the manager. We need competition."
Cole initially joined West Ham in 2006.