De Zerbi has taken the Seagulls to new heights ever since replacing Graham Potter at the helm last year as he led them to a sixth-place finish in the Premier League and straight to the Europa League.
The Italian tactician’s impressive work at the AmEx, though, has attracted interest from his home country, with Napoli and AC Milan keeping tabs.
The 44-year-old has also been linked with some of Europe’s biggest clubs, such as Real Madrid.
Reports even suggest Manchester City have identified the former Shakhtar Donetsk boss as Pep Guardiola’s eventual replacement when he leaves the Etihad.
Brighton want to hold on to De Zerbi for as long as possible, with his contract running out in 2026.
But Barber insists the Premier League outfit has a succession plan in place just like they did when Potter left for Chelsea.
The Italian was at the top of their wishlist long before they even started looking for a new manager.
Barber told talkSPORT: “Good players and good staff will always be looked at by competitors, and we’re prepared for that, we’re realistic about that and we try to plan for those eventualities.
“When we unfortunately lost Graham Potter to Chelsea it was a difficult period, because you don’t want to lose your head coach one month into the season. We always have a small list of coaches that we would look to move to if we had to, Roberto was top of that list.
“So far things have worked really well, we’re enjoying what Roberto is doing for us and what this squad of players is delivering. Roberto has done a fabulous job and I don’t think anyone in world football hasn’t seen the way he plays and the way we play.
“The biggest conundrum with our model is the better we do, the more vulnerable we become, because people look at what we’re doing, how we’re doing it, the people who are doing it for us, and they want them.
“We’ve seen that many, many times, whether it’s Alexis Mac Allister to Liverpool, Moises Caicedo and Graham Potter to Chelsea, Yves Bissouma to Tottenham, and staff we’ve lost along the way as well, Dan Ashworth to Newcastle – it’s on and off the field.
“But I take that as a big complement to the progress we’re making and it’s incumbent on me to make sure we’ve got succession plans in place to manage and overcome those bumps in the road.
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“Because at the end of the day every football club will lose players and staff at some point, we just have to make sure we’re ready and prepared for it when it happens to us.”
Asked if Brighton already have a replacement in mind in case De Zerbi leaves: “Absolutely.
“That’s part and parcel of looking at the top 20 or 25 positions in our club all the time and identifying who’s vulnerable to being taken by somebody else or who may simply just want a change in lifestyle and making sure we know if that happened who would be coming in to replace them.
“That might be an internal appointment or an external appointment, but the most important thing is that we have an idea who it would be.
“There’s nothing worse than suddenly facing a change and then having a gap because you haven’t done the homework to consider who would replace that person. Preparation is critical.”