Verstappen has been highly critical of Red Bull and Renault recently after a spate of car problems in 2017, hinting that he wants to break his contract.
Mass, a veteran of 114 grands prix and a single win, told T-Online: "Verstappen is too convinced of himself.
"I think it's because the hype about him all came far too early. He was praised to heaven after his victory in Barcelona (2016), but he won with a lot of luck.
"Now miracles are expected of him.
"Sure, Max is a talented boy, but we will only see how good he really is in the future."
Verstappen is currently sixth in the driver rankings.