The attacker has angered De Zerbi with his attitude and the Brighton boss, unhappy with the Belgian’s displays at training ahead of last weekend’s FA Cup tie with Middlesbrough, told him to train alone this week.
De Zerbi confirmed on Friday that Trossard will not be involved against Liverpool in the Premier League this weekend.
Trossard has emerged as a target for Tottenham amid fierce speculation over his future this month and he has now left the UK.
He got onto a Eurotunnel shuttle with his car on Friday afternoon and it is not clear whether De Zerbi authorised the trip.
If De Zerbi did not give Trossard permission to travel abroad, it could signal a further damaging twist in what appears to be a failing relationship between manager and player.
Tottenham want to bring in a new attacker this month and Trossard is a potential addition.
Trossard has just 18 months left on his contract at Brighton and as such now may be the optimum moment for the Seagulls to cash in.
