The Italian could be in place for the Seagull's next match against Liverpool on October 1 after holding positive talks with the Premier League side.
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De Zerbi, 43, made his reputation at Sassuolo with some thrilling football and impressive scalps against Serie A giants during his three-year spell.
The former midfielder left the team from Emilia-Romagna in 2021 before taking over the reins at Champions League regulars Shakhtar Donetsk, but his stint in Ukraine was cut short by Russia's invasion of the country.
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With De Zerbi currently unemployed, he may prove to be an easier deal than Brighton's other lead candidate Bo Svensson, with Mainz keen to keep the Dane in Germany.
Seagulls owner Tony Bloom wants to appoint Potter's successor before Brighton's next Premier League game at Anfield after the international break.
Bloom had seen his side begin their league season brilliantly with four wins and a draw from six matches, but that stability was rocked when manager Potter was targeted by Chelsea.
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The Blues moved swiftly to take the Englishman from the AmEx stadium, with Brighton planning on giving midfielder Adam Lallana a player/manager role while they searched for a replacement.
But due to the postponement of their clash with Crystal Palace, Brighton won't play again for two weeks, and could have a new face in the dugout by the time their next fixture rolls round.