Southampton are looking to appoint their new boss
It is understood the 62-year-old Chilean was keen on the move but the club are looking at other options to replace Ronald Koeman.
According to BBC Sport, Frenchman Claude Puel, 54, is reportedly the favourite to take over after leaving French Ligue 1 side Nice at the end of last season.
Dutchman Koeman left to join Everton earlier this month after two campaigns at St Mary's.
United States head coach Jurgen Klinsmann is also not being considered despite being linked with the job.
Bournemouth boss Eddie Howe, former Manchester United manager David Moyes and ex-Ajax head coach Frank de Boerare all out of the running too says the BBC.
Southampton are looking to appoint their new boss by the time players report for pre-season training next week.