De Zerbi opted to start the Sweden international for the first time in Spurs' preseason campaign as they won a penalty shootout after a 1-1 draw with Sydney FC.
Bergvall has found himself at the centre of transfer interest from several clubs - with Newcastle United reportedly seeing £46M bid rejected for the 20-year-old - after they sold Sandro Tonali Spurs for £100M.
De Zerbi has been bullish over his lack of flexibility on retaining players who want to leave, and that is his message to Bergvall, despite his desire for the towering midfielder to stay in North London.
"Lucas has never said that he wants to leave and I'm speaking to him every day.
"I would like him to stay with us, as I think he has the potential to be a top, top player.
"But, I don't want to have to convince anyone to stay here. Tottenham is a top club and we shouldn't have to convince anyone.
"I hope he stays as it's not easy to find a young player at that level."