Redknapp is the media's overwhelming favourite to replace Fabio Capello, who resigned as England boss on Wednesday.
This has led to speculation as to who may replace the 64-year-old at White Hart Lane.
Moyes, who has been the Toffees manager since 2002, is the 7/2 favourite at Skybet to be the next man in charge at Spurs.
However, Everton defender John Heitinga is hopeful that Moyes will stay at Goodison Park.
He told The Mirror: "Moyes is the right man for us. What he has done is unbelievable."
Meanwhile, Redknapp has claimed that he remains focused on continuing his job at Spurs.