Koeman gave Vermaelen his professional debut when in charge at Ajax way back in 2003 and reports claimed that the former Dutch international was keen on a reunion with the defender this summer.
Everton made a last-ditch bid to sign Vermaelen on transfer deadline day in the summer, but the 31-year-old would not be drawn into commenting on that when talking to 'Sky Sports News'.
"I don't want to go into details," he explained.
"Barcelona always said they didn't want to let me go. All big clubs need at least four centre-backs.
"They were happy with my pre-season and kept me."
The former Arsenal man did open up slightly more when questiond about the pressure that Koeman is currently finding himslef under at Goodison Park, saying that he has no doubt that Koeman can get the 'Toffees' out of their current rut of form.
"He's shown at Southampton and Ajax that he's a great manager," said Vermaelen. "He has the experience to turn it around for sure."
Everton fans will be hoping that the Belgian is right.