The reigning constructors' champions have already been dealt a significant blow in losing their design guru, and can ill-afford to see Verstappen move on as well.
Ecclestone, however, believes Verstappen would be 'silly' to be considering other options, and insists Red Bull is the best place for him to build his legacy.
The 93-year-old said: "He's too intelligent to do that [leave]. What would he gain? To go where?
"It'd be silly to move. There's nowhere he could go where I think he would get exactly the same service as you get at Red Bull."