According to Sky Sport24, the under-fire Biancocelesti boss informed the club of his decision to step down via fax on Wednesday.
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According to reports, though, Reja's future remains uncertain and it has been claimed that, unless the Biancocelesti overturn their 3-1 first-leg deficit against Atleti, the 66-year-old Italian will part company with the club on Friday.
Reja has endured a fractious relationship with the Lazio board and he is said to have clashed with president Claudio Lotito over the club's parsimony during the January transfer window.
The coach offered to walk away from the Stadio Olimpico after a home defeat by Genoa back in September, but he was talked into staying by both Lotito and the club's players.
Lazio were routed 5-1 in Palermo at the weekend but remain fourth in the table, level on points with third-placed Udinese, and still well in contention for a Champions League place.
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