Fly-half Wilkinson has not played since suffering his second knee injury of the season during Newcastle's Zurich Premiership defeat against Harlequins almost four weeks ago.
His latest fitness setback cast doubts over him making the Lions tour to New Zealand this summer.
But although he will not be involved in Falcons' Premiership appointment with Worcester on Sunday - 24 hours before Woodward announces his squad - a return against Northampton next week must be distinctly possible.
"Jonny is about as close as you can get, without actually being there," said Andrew. "We have got to do the right thing and ensure he is 100 per cent."
Woodward, though, will be thrilled about the return of Newcastle's Welsh international flanker Colin Charvis this weekend.
Charvis, Wales' outstanding player during their autumn Test matches, has not played since suffering a serious foot injury some three months ago, missing the entire Six Nations Championship.
But he is back in the Falcons starting line-up on Sunday, taking over from Mike McCarthy at blindside.