The British & Irish Lion is back in training with his club Newcastle but he has not made the Falcons 22 for their European Challenge Cup clash against Borders at Kingston Park on Sunday.
"Jonny has trained this week and he is getting there," said Newcastle rugby director Rob Andrew.
"But the more I say on the subject, the less chance he seems to have of playing. So this week, I will just keep my mouth shut and let him get on with it."
Fly-half Wilkinson has not played since mid-November, while his last England appearance came in the 2003 World Cup final before a series of injury setbacks put him out of the international picture.