The 33-year-old underwent surgery just over six weeks ago to mend what had been an ongoing shoulder injury.
Some reports had claimed that he may struggle to make the start of the upcoming campaign, but the England international has insisted that he is likely to be able to return to training in "a couple of weeks".
"It's going well and feeling strong," he told the club's official website "I'm six weeks down the line with the rehabilitation from surgery.
"I'm not too far away, maybe a couple of weeks away from contact and being back in full training if everything goes well. I'm looking forward to it.
"It's probably the longest break I've had at this time of year. Being out of the game for six weeks is enough, I'm itching to get back."
The Reds open their Premier League season with a home match against Stoke City on Saturday, August 17.