Cole, 29, has featured in his team's wins against both Guangdong and Malaysia XI.
"I've been happy with my performances," he said. "Now I just want to get started. I feel great physically. I'm happy with how I'm performing and I want to get a couple of 90-minute run-outs under my belt."
The midfielder, who has 56 England caps, will have to contend with new signings Charlie Adam, Jordan Henderson and Stewart Downing.
However, Liverpool assistant manager Steve Clarke still believes that Cole can make an impact at Anfield.
"He's looked good in both matches we've played so far and Joe Cole is a top international player," Clarke explained. "He's got a big contribution to make in the future."
Liverpool's next pre-season fixture is against Hull City on July 23.