Wilkinson, a 2001 British & Irish Lion who will undoubtedly be in Sir Clive Woodward's thinking for New Zealand, will be given every opportunity to recover in time as Newcastle are not obliged to name their side until Thursday afternoon.
However, Black was not overly optimistic.
He said: "I think it would be a huge ask at this point.
"It is all going very well and I am very pleased, but whether he will be ready for the game in Paris on Saturday is a big ask, it really is.
"I am not pulling the wool over anyone's eyes.
"You would never rule him out of anything, but from a realistic standpoint, that would be a big ask."
Wilkinson suffered a recurrence of an old knee injury on his return to action against Harlequins three weeks ago.
Newcastle director of rugby Rob Andrew revealed after the defeat by Bath on Sunday that England's World Cup-winning fly-half would be given every opportunity to overcome the setback and he could yet figure at the Parc des Princes.
That he is still in contention suggests Wilkinson's recovery is progressing ahead of schedule.
But Wilkinson has suffered four serious injuries since the World Cup and Black is aware how important it is to manage his return successfully.
Black told BBC Radio Five Live: "He's a very sensible young man.
"He is very passionate about the game and very passionate about the club he plays for but we have got to do what is best for him in the long run."
"He is a national treasure and we need to do whatever is right for him and his career."
The fitness of Wales flanker Colin Charvis, another potential Lions tourist, is also being closely monitored although Saturday's encounter may also arrive too soon.
Charvis missed Wales' charge to Grand Slam glory with a foot injury and Black added: "We'll not try to press the fast forward button even though this game's very, very important.
"Jonny and Colin will come back when they're ready."