The Spanish left-back has been out of action since being forced off before half-time during the Reds' 7-0 Champions League win over Spartak Moscow on December 6.
The 25-year-old says he is not feeling 100 percent but is just happy to be back out on the training pitch with the rest of his team-mates.
"I can still feel it's not quite right but it's getting better every day and the good thing is that I'm training with the rest of the group," he told the club's website.
"We're just waiting for this little discomfort to go away and then I'll be raring to go."
Moreno says he does not yet have a potential comeback date in mind, meaning Saturday's FA Cup fourth-round tie with West Brom is likely to come too soon.