Smith then made the decision to hand the teenager his bow in the Champions League when he partnered David Weir in the heart of defence as Rangers earned a 1-1 draw with Unirea Urziceni in Bucharest on Wednesday.
Rather than being fazed by the occasion, Wilson stole the show with one of the top performances of the night and is now expected to make his first Ibrox appearance against St Mirren on Saturday.
For Smith, the comparisons with Narey are obvious. The defensive lynchpin of the successful Dundee United team of the 1980s, Narey was also just 17 when he made the breakthrough to senior football.
"I was surprised, not just by the way Danny Wilson played, but by how he handled the overall situation," admitted Smith.
"He didn't look fazed by it at all and there were no great signs of nervousness in the first few games he has had.
"I was fortunate at Dundee United to have David Narey and he is a similar type of player to him and has a similar attitude.
"If he can have as good a career as David Narey had, then we will all be happy.
"We are delighted by the manner in which he has played. He has shown he has been able to progress from youth football into the first team.
"I was hoping he would get a few games this season and it's looking as though, if he continues to play in the manner he has done, he will get a lot more than I envisaged at the start of the season."
Wilson's performances may have propelled him into the spotlight but Smith is confident he possesses the maturity to deal with the sudden attention.
"There is a tendency for people to get carried away," said the Rangers boss.
"But he is not the type of boy that looks as though he will. He is very steady in his approach to everything.
"While I feel I was forced to put him in a little bit early, he has shown there was no real major worry about that.
"He has come into the team and, for a 17-year-old boy, played extremely well in three different types of games.
"He has handled it all and has played very well to boot. Hopefully that can continue.
"It will be nice for Rangers supporters to see one or two of our younger players coming through. John Fleck is another one who is now ready to play as well.
"If we are talking about having a smaller group this year, it has certainly given some of the younger players an opportunity, although both these boys would have had that opportunity regardless anyway."
Looking ahead to the visit of St Mirren, Smith added: "I always think they play to a good level and I was surprised they were fighting relegation last season.
"I think Gus MacPherson could be doing with a bit of help in terms of a little bit of money spent to bring in one or two better players to help lift them again.
"That's the only thing that has been holding them back recently. He deserves great credit for the way he has handled his team over the last few seasons."