The former Rangers midfielder is being mentioned in connection with the vacant position at Ibrox.
Parlour and Van Bronckhorst, who spent three years as a Rangers player, were at Arsenal together in the early 2000s.
Now in charge of another of his old sides, Feyenoord, the Dutchman was surprisingly linked with the vacant Rangers position earlier this week.
But he is now second favourite for the role with bookmakers Sky Bet, leading many people to believe his appointment is possible.
Speaking on Thursday's Jim White show [10:07], Parlour said of Van Bronckhorst: "He'd be a great appointment for Rangers, I think he's done brilliant at Feyenoord.
"As a player he was a very intelligent guy when he first came to Arsenal. He understood the football, the way you had to play. You could always see him going into coaching. He was one of those guys that loved the football, he always had something to say when we had meetings, even if he wasn't playing.
"I don't think they would go far wrong with Giovanni - whether he wants to go there."
Van Bronckhorst remains a popular figure at Rangers and, according to Parlour, he has equally fond memories of his time at Ibrox.
"He knows Rangers, he's played for Rangers. When he came to Arsenal he had high praise [for] Rangers, he said it was a great club, well run, fantastic people, and I'm sure if he got the opportunity that could be a really good job," added the Englishman.
"He could go to try and compete with Celtic again. They'll have to have quite a bit of money to spend, maybe, [in] the transfer market, to bring in some players he knows. Maybe he looks at Holland and says I know a lot of players in Holland now, I've been a manager here. There's a lot of players who could probably step up and go and play for Rangers."
Feyenoord gave Van Bronckhorst his first managerial role two years ago and the 42-year-old has since rewarded them with one KNVB Cup and an Eredivisie title.
Were he to leave the Dutch giants for Rangers, he would be following the same path he took as a player 19 years ago.
Would Van Bronckhorst leave Feyenoord for Rangers?