It was feared the Dutch international had to undergo ankle surgery and miss a big part of the season.
But the 30-year-old should be back playing in a month as he does not need ankle surgery.
Kuyt said: “I had a second scan and the doctor has now told me that they do not need to operate on my ankle. That is such a relief.
“The doctor says I could be back in the Liverpool team within one month.”
He added: “I can’t wait to play again and help the team.
“The doctor says this injury needs a bit of rest and good physiotherapy will speed up my comeback on the pitch.”