Trossard left training without permission having been informed he would not start last weekend's FA Cup third-round tie against Middlesbrough.
The Italian coach remains open to reconciliation with Trossard, who has been linked with a move to top-flight rivals Tottenham this month, but will not currently consider him for selection due to his unprofessional behaviour.
"Leandro isn't in the list of players for tomorrow," De Zerbi said ahead of Jurgen Klopp's Reds visiting the Amex Stadium.
"The last training session before the Middlesbrough game when he understood he didn't play, he left the session without saying anything to me. And it's not good.
"The Monday after, I spoke with him and I explained this attitude, this behaviour, I don't like.
"He knows very well that if he wants to play with Brighton with me, he has to work hard, he has to run, he has to be in the right way because we are not a big team such as Real Madrid or Barcelona, we are Brighton and we need players who work like the others who stay in Brighton.
"I don't know what is the problem. I want to be clear; I am open with him to take a step back and listen to him but he has to understand with me, I want only players who work hard and play for the team 100 per cent."
Trossard has hit seven Premier League goals this season - including a hat-trick at Anfield in October - to put the Seagulls in contention for European qualification.
After starting Albion's first two league games following his return from the World Cup, the forward was an unused substitute for the 4-1 win at Everton, before his omission at the Riverside Stadium.
Brighton are not under imminent pressure to sell as they hold an option to extend his contract until 2024.
"I don't know about the transfer market, if he wants to change teams or not," said De Zerbi. "It's not my problem. I'm only a coach.
"I'm not thinking about the transfer market, the other teams, or other discussions. The only discussion is to play for the team and to work and to run on the pitch.
"Leo is one of the best players in this squad - I understand something about football.
"But I know also to achieve the result we have to be a group and to think for the team before ourselves. This is (one of) the first rules in my head."