The Sweden international had been strongly linked with a summer exit, with Nottingham Forest and Newcastle United both tabling significant bids that Tottenham rejected, while Chelsea, Manchester United, Borussia Dortmund and Bayern Munich were also credited with interest at various points.
Instead, it was the 20-year-old midfielder who moved to draw a line under the speculation.
Speaking to Sky Sports, De Zerbi said Bergvall and his representatives approached the club directly once pre-season training was under way.
"After ten days in pre-season, he and his agent went to [sporting director] Johan Lange to say that Lucas was happy to stay," said De Zerbi.
"Lucas showed me that he wants to stay. I would like to play with him, to put the focus on him. In terms of the player's potential, he is another top player."
The picture is very different for Richarlison, who is edging closer to an exit from north London. The 29-year-old Brazil international is reportedly closing in on a move to Trabzonspor in Turkey, with De Zerbi confirming the forward had made his desire to leave clear throughout pre-season.
"Richarlison decided everything on his own. He spoke to me at the start of pre-season, he told me his idea, his wish was to leave," De Zerbi said. "We went to bring in another striker and, as I said at the start of pre-season, I only want to keep players who want to stay with the right passion to be here.
"I can't say anything because I didn't decide anything. Richarlison's message from the start of this season has been very clear. I accepted it," the coach added.
Bergvall joined Djurgården from Brommapojkarna in 2023 before completing his move to Tottenham for a fee reported at around £8.5m the following year, and has since made over 50 appearances for the north London club.
According to Swedish outlet Fotbolltransfers, Djurgården negotiated a resale percentage as part of that original deal, meaning the Allsvenskan club came close to a significant windfall this summer before Bergvall opted to stay and the clause went unused.