The 19-year-old has been out of action since September after hobbling off during the Capital One Cup third-round tie against Doncaster Rovers after making just three appearances for the Canaries.
Kane headed back to White Hart Lane for treatment but looks set to return to Norwich and could be in the squad to face Chelsea and Manchester City over the festive period.
"Harry has completed about five days training in total, four of them with Tottenham. He is at the stage now where he has to keep developing his fitness,” Hughton told Sky Sports.
"We have to determine over this next week or so when he is available for games. I think he has done a lot of good rehab, which is good news for us.
"I feel for the lad because he came here with a real spring in his step. The good thing is he is young and the type of injury he had, he will make a full recovery from, possibly for Christmas, but it is too soon to assess yet. He needs a week's training."
Norwich host Wigan on Saturday looking for a fifth-straight league win, and Hughton has dismissed talk of the midweek 4-1 loss to Aston Villa in the Capital One Cup having an adverse effect on the squad.
He added: "It wasn't difficult to pick them up because we are on a good run at the minute.
"We had managed to get ourselves into the quarter-finals of the cup competition and were probably just beaten on the day by a more clinical side.
"We have done well. I can't fault the endeavours of the lads, but it wasn't to be. We have to get back to basics and continue the league form."