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Sevilla head coach Lopetegui has rebuilt his reputation with the LaLiga club after being sacked by both Spain and Real Madrid in 2018.
Last season he led Sevilla to a fourth-place finish and Champions League qualification, having won the Europa League in 2019-2020.
Spurs' fraught search for a long-term successor to Jose Mourinho has taken in links to Mauricio Pochettino and Antonio Conte, appeared close to a conclusion during discussions with ex-Roma boss Paulo Fonseca and descended into farce when fans protested against the prospect of appointing Gennaro Gattuso, the former Milan and Napoli head coach.
And, if Castro is to be believed, Lopetegui is not about to answer Tottenham chairman Daniel Levy's call.
"Julen rang me and told me," Castro told Cadena SER regarding an offer he described as "dizzying".
"Some coaches are more driven by economic factors but Julen is very clear that he is happy here and he even said it would be very difficult to find a better place to work than here.
"We believed and believe in him, giving him a two-year contract extension, and I'm sure he will bring much more to the club."
Uncertainty at Tottenham has not been helped by speculation over star striker Harry Kane being unsettled, with Manchester City reported to have tabled a £100million bid for the England captain this week.