The Italian led Brighton to a sixth-placed finish in last season's Premier League, with the Seagulls therefore playing Europa League football this term, and they reached the knockout round of the competition.
It has been more difficult for the club this term, with 44 points from 32 matches leaving them down in 10th spot in the table, six points behind sixth-placed Newcastle United.
De Zerbi's work since arriving at the Amex has seen him linked with a number of the top jobs in world football.
Both Liverpool and Barcelona are currently searching for new managers to begin this summer, as Jurgen Klopp will stand down from his role at Anfield, while Xavi is preparing to leave Camp Nou.
De Zerbi has no intention of leaving Brighton
Manchester United could also be on the lookout for a new head coach at the end of the season, with Erik ten Hag's position at the helm far from secure due to the team's struggles.
All three clubs are thought to be interested in De Zerbi, who was in charge of Shakhtar Donetsk before his arrival at Brighton, and he has now taken charge of 83 games for the Seagulls.
The 44-year-old has a record of 37 wins, 21 draws and 25 defeats during his time at the Amex, which has given him a win percentage of 44.58.
However, amid the speculation, De Zerbi has said that he is not planning to move on, having "made a commitment", penning a contract at Brighton until June 2026.
"I love Italy and our football," he told Bobo TV. "I feel good in England, in the Premier League and I have no intention of leaving. There is no team that can change my mind, I have made a commitment.
"I like being outside and experiencing the atmosphere of the stadium. Furthermore, in England, I have the opportunity to improve my knowledge of the language and football."
Brighton drew 1-1 with relegation-threatened Burnley in the league on Saturday, with an own goal from Arijanet Muric cancelling out an opener from Josh Brownhill.
"It is a fair result. We didn't deserve to win or lose. I think in this moment Brighton are like this. We are trying to win and play better but it is clear we are spending a tough moment because we have a lot of injuries," the Italian said in his post-match press conference.
"We suffered in the first 20 minutes but after that time I think we played a good game, not great but we are not in the right condition to play great games at this time. It's a tough moment but we have to fight and play with pride."
Brighton will be aiming to end a four-game winless run in England's top flight when they welcome the champions Manchester City to the Amex on April 25.