The attacking midfielder has so far made seven appearances for Cheltenham since arriving on November 20.
"Since I have come in, Kane has gone from strength to strength," boss Paul Buckle said.
"He can play in central or wide areas as well as in the number 10 role in the space, which we like.
"He's been great and I feel he is one who has improved on the back of what we are trying to do here."
Ferdinand's extended loan spell is subject to the completion of paperwork.