The Dutchman spent three successful seasons as a player during Gordon Strachan's spell in charge and the impressions made in that time have stuck by him.
In his eyes there are certain standards that need to be upheld by whoever follows Neil Lennon into the job, and a former player would probably be the best candidate to meet those criteria. He is not putting himself forward - far from it - but if someone like Henrik Larsson, Malky Mackay or Paul Lambert were to end up getting the job then Vennegoor of Hesselink believes they would be a better fit than any unconnected candidate.
"I think it needs to be a coach who has a little bit of a Celtic history," he said on his return to Scotland to participate in a footgolf competition at Cowal Golf Club. "Celtic is a club that comes with a handbook. It's not a club where you can go in and say, "let's start fresh". It has a history and a fanbase with expectations.
"It is not the easiest of coaching or management jobs. There is a lot of pressure on. Last year, Lenny won the title quite easily but there was still pressure with getting into the Champions League and trying to get results there. I think it needs to be a coach with a little bit of history with the club - but that is only my opinion."
Were nostalgia a key factor in the recruitment of the new Celtic manager, then Larsson would win by a landslide. The Swede's popularity remains undiminished in the decade since he left the club for a new challenge, and his appointment would likely be met with a huge rush of acclaim even if his coaching credentials are still unproven.
Sometimes certain figures find themselves repeatedly drawn to the same club, the way Johan Cruff was to both Ajax and Barcelona, and Vennegoor of Hesselink wondered if there was something inevitable about Larsson one day sitting in the home dug-out at Celtic Park.
"I think Henrik is the fans' choice," added the 35 year-old who retired from playing two years ago. "I think everyone would like to see him back. If he was to come it would be a huge thing. But I don't know whether he feels ready for it himself. He is a manager just now in Sweden.
"I read that he had talked about coming back to Celtic at one time but we'll have to wait and see what happens. He has such status within the club with the fans. He'd always get the time and have the backing of everyone. If you look at his record and everything he did, it's too obvious. It doesn't matter who you ask, everyone would say the same.
"I read that one day he could return to Celtic and like Cruyff with Barca or Ajax they are destined to come back together."
Vennegoor of Hesselink's first season at Celtic was also Lennon's last as a player; the pair reunited a year later when the Northern Irishman returned as a first-team coach. He has been impressed with the way his former colleague grew into the manager's role, delivering silverware as well as recruiting players who would be later sold on at huge profit. There is also an understanding why, after four years, Lennon has decided to call it quits.
"I think what Lenny did after four years means he can hold his head high," added the Dutchman.
"He decided for himself to stop - there were no strange things or bad results. He said it was time and everyone - more or less - will think it's okay because he was open about the decision. He did a really good job when you look at players and also achieving goals in the Champions League and winning the league.
"It looks sometimes from the outside like a simple thing, but getting to the second round a couple of times with the finances means it's a really good job he did. If you look at the records in time you will appreciate the job he did at the club."
The need to bring players in on the cheap and sell them for massive profit chimes with Vennegoor of Hesselink. It is a similar story in Dutch football where the sums of money involved are dwarfed by those in England and Germany.
"Ten years ago you could build a squad and keep them together for five years and try to do something in Europe," he added. "Now you can't hold the players back when a big club comes in - for example when Luis Suarez left Ajax to go to Liverpool. If a club from the Premier League comes in it's hard as the clubs need finance. It's the same in Scotland - you can't spend big money on big players with big salaries. You have to hold yourself to a strict budget and that's how it is."
n Vennegoor of Hesselink was speaking ahead of his participation in today's Scottish Footgolf Open in Dunoon, the first event in Scotland for the hybrid sport combining football and golf. The Scottish Footgolf Open is supported by PA23, a Business Improvement District campaign to bring events and projects to the Argyll town. The event takes place at Cowal Golf Club in Dunoon and Footgolf hopes to recruit more courses across Scotland in the near future.