The England centre-half made just three appearances for Spurs last season as he was hampered by more injury problems.
The 30-year-old is out of contract at the end of the forthcoming season and Spurs are losing patience with him.
Harry Redknapp (talking to the Daily Telegraph): "It's make or break for Jonathan now.
"He has got to come back and play. If he is not ready for the start of the season it will be difficult for him. When he gets his boots on and starts playing hopefully he will be all right.
"He is a fantastic player: one of the best centre-halves around. We just take it day by day with him and see how he progresses."