The move comes with former Barcelona midfielder Oscar Garcia expected to be named interim Seagulls boss, to replace the sacked Gus Poyet, by Thursday.
Garcia's former club Maccabi Tel Aviv have announced that assistant boss Ruben Martinez and fitness coach Juan Torrijo Navaro have left to "continue their partnership with Oscar Garcia".
And Brighton have confirmed former Tottenham defender Taricco, who has been overseeing pre-season training after having his recent suspension by the club lifted, has left by "mutual consent".
Poyet, himself suspended by Brighton last month along with Taricco and coach Charlie Oatway, was axed on Sunday night following a disciplinary hearing into an alleged breach of contract.
Poyet is set to appeal against the decision so Brighton can only appoint an interim boss.
But it is understood the club intend to make Garcia, who quit as Maccabi head coach last month after guiding them to the title, their permanent manager once the dispute with Poyet is settled.
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- Gus Poyet