The 31-year-old, who was ruled out for six months with a groin injury, has been used as a substitute for the Reds' last three matches, but has yet to play a full half for the Merseyside club.
"For Steven it's just a progression," Clarke told the club's official website. "He's coming back from a long-term injury and we'll try to treat him as cautiously and carefully as we can.
"Obviously there will be a time when he is going to have to push on - and I think this is the time now.
"He's going to have to push himself in the coming weeks - and the more minutes we get into him, the better."
This could pave the way for the England international to play a role in the Reds' clash with rivals Manchester United on October 15.