Richarlison is one of three players who De Zerbi says have asked to leave Tottenham.
He, Kevin Danso and Pape Matar Sarr have all been linked with moves away from Spurs and none were included in De Zerbi’s match squad as Tottenham lost 2-0 at home to Newcastle on Saturday.
Asked about their status after the loss, De Zerbi said: “Richarlison, I don’t know. He said too many times he wants to leave.
“Danso came to me two days ago and he said wants to leave and Pape Sarr the same, but he suffered a small injury, but he is almost ready to train.
“I have very good relationships but if they want to leave, they have to bring the solution, the economic solution, to the club, and they can go.”
Spurs have spent more than £300m this summer in an effort to restore their competitive edge following back-to-back 17th-place Premier League finishes.
But Tottenham are bottom of the table, having lost their first two games to Brentford and Newcastle and failing to score a goal.
With 11 goals, Richarlison was Tottenham’s top scorer last season and a key figure during their struggle for Premier League survival, which was secured on the final day.
Earlier in August, De Zerbi said that the Brazilian was uncertain about his future, noting that “it’s not easy to find another striker like Richarlison”.
Last week, Manchester City striker Omar Marmoush joined Spurs on loan and he replaced Richarlison in De Zerbi’s starting XI against Newcastle.
Danso’s first-team opportunities may be limited this season as Marcos Senesi and Jan Paul van Hecke arrive to challenge for his place in central defence, where Micky van de Ven’s spot was secured by the signing of a new contract and the award of the captaincy.
Sunderland made an offer to take Danso, who has 36 Austria caps, on a season-long loan – but Spurs rejected it.
In midfield, Sarr’s chance to play has been impacted by the arrivals of Mateus Fernandes and Sandro Tonali early in the window, as Tottenham kicked off their a statement summer of transfers by breaking their club record fee twice in one week.
The Senegal international, 23, has attracted interest from a number of clubs, including several in the Premier League and Turkish side Besiktas.
However, Juventus are understood to be confident of winning the race for his signature on a loan deal that includes a conditional obligation to buy.