The Govan club confirmed on Thursday that the 46-year-old former Light Blues player will become Steven Gerrard's successor subject to receipt of a work permit.
Van Bronckhorst worked under fellow Dutch manager Koeman at Feyenoord before stepping up to become boss while Wilson worked with Koeman at Southampton.
And when it came to getting some thoughts about the former Arsenal, Barcelona and Netherlands player ratified, he made the call to Koeman and got the expected assurances.
Wilson told Sky Sports Scotland: "I wouldn't say he played a part in luring him but he is certainly someone I spoke to about Gio because I knew how much respect he had for him.
"So to be honest, it was a phone call I was making when I probably already knew a lot of the answers.
"Gio is somebody that Ronald always spoke highly of and someone I keep in regular contact with, someone whose opinions I would trust wholeheartedly as well.
"He is a great man himself, he has high standards and when he gives me positive insight into someone else then I can take that as something I trust a lot."
Van Bronckhorst, who won two league titles, two Scottish Cups and a League Cup during his three seasons as a player at Rangers, will be in the stand for the Premier Sports Cup semi-final against Hibernian at Hampden Park on Sunday.
Player-coach Jermain Defoe, B-team boss David McCallum and his assistant, Brian Gilmour, along with goalkeeping coach Colin Stewart will be on the sidelines and Wilson has confidence in his stand-in management team.
He told RangersTV that Van Bronckhorst was "excited for the game" then addressed the situation regarding the Hampden dugout.
He said: "We have a number of really talented staff working for us here.
"I am proud of the backroom we have assembled here, many people have contributed towards building that backroom, I have led them every day for a while and have great pride in the work that they do.
"We have great people here at Rangers and they will be the key people involved, supported by all their staff on Sunday."