De Zerbi focused on Brighton's battle for Europe amid Spurs links
Conte's contract expires in the close season and the Italian manager's future at Spurs is up in the air after the north London club were knocked out of the FA Cup and Champions League, leaving them with nothing to play for but a top-four finish.
Fellow Italian De Zerbi signed a four-year deal when he took over at Brighton in September, replacing Graham Potter who joined Chelsea, continuing a revival in the club's fortunes with an attractive style of football.
"I have a long contract with Brighton and I'm happy to work here. I'm enjoying working with these players," De Zerbi told reporters when questioned about the links ahead of Saturday's Premier League clash away at Leeds United.
"I'm delighted with the performance of my players. We have a dream and we know we can write a new history for the club. That's very important for us and a nice challenge."
Brighton, who gained promotion to the Premier League in 2017, have never played in European competition.
De Zerbi's side are on an impressive run with four wins in their last seven games to sit eighth, four points behind fifth-placed Liverpool having played two fewer games.
"I am really pleased for my players and I am happy for their performances and results," he added.
"We want to arrive in Europe but we have to push and take it game by game. Tomorrow starts a difficult period with three games in a week, but we are ready to fight for our targets."