The Italian, who replaced Graham Potter at Brighton in 2022, has been linked with soon-to-be-vacant jobs at top European clubs including Bayern Munich, Barcelona and Liverpool.
Bayern's Thomas Tuchel, Barca's Xavi Hernandez and Liverpool's Jurgen Klopp are set to leave their jobs at the end of the season.
"I am still proud to be coach at Brighton," De Zerbi told reporters.
"I know I am really lucky to work with these players, to work with this club. I'd like to compete with a full squad but I try to play with the players available and I think they are enough."
De Zerbi's contract with Brighton expires in 2026.
The former coach of Ukrainian team Shakhtar Donetsk and Serie A's Sassuolo said last week that he would speak to Brighton's owners before making a decision.
"It's (future) not a problem, it's a part of my work. At the moment I want to be focused and to keep my eyes on the target we have. I have the contract at the moment. The focus is on the pitch," he said.
"I'm very relaxed. The problems are the injured players and the preparations for the next game. These are the problems not the contract or my future."
Brighton, ninth in the Premier League with nine games left, visit 15-placed Brentford on Wednesday.
