The Greek forward first arrived at Parkhead on a six-month deal from Manchester City in January 2008 and Vennegoor of Hesselink admits he is surprised to see that the now 28-year old remains in Glasgow more than five years later.
"Sami is almost Mr Celtic these days. It is unbelievable," the Dutchman said.
"He has had a lot of highs and lows at Celtic and that is something every player experiences.
"But he has already been at Celtic for over five years. Who would have thought that would happen?
"Sami just enjoys being a Celtic player. It is a big compliment for him that he has stayed so long.
"It looks like he has found a home. It is a Greek and Glasgow love story!
"He is important in the big games and he is a character around the squad.
"Some players are real leaders and do it in a natural way. Sami is now in that role for Celtic."